In quadrupeds,the cervical and lumbar circuits work together to achieve the speed-dependent gait expression.While most studies have focused on how local lumbar circuits regulate limb coordination and gaits,relatively ...In quadrupeds,the cervical and lumbar circuits work together to achieve the speed-dependent gait expression.While most studies have focused on how local lumbar circuits regulate limb coordination and gaits,relatively few studies are known about cervical circuits and even less about locomotor gaits.We use the previously published models by Danner et al.(DANNER,S.M.,SHEVTSOVA,N.A.,FRIGON,A.,and RYBAK,I.A.Computational modeling of spinal circuits controlling limb coordination and gaits in quadrupeds.e Life,6,e31050(2017))as a basis,and modify it by proposing an asymmetric organization of cervical and lumbar circuits.First,the model reproduces the typical speed-dependent gait expression in mice and more biologically appropriate locomotor parameters,including the gallop gait,locomotor frequencies,and limb coordination of the forelimbs.Then,the model replicates the locomotor features regulated by the M-current.The walk frequency increases with the M-current without affecting the interlimb coordination or gaits.Furthermore,the model reveals the interaction mechanism between the brainstem drive and ionic currents in regulating quadrupedal locomotion.Finally,the model demonstrates the dynamical properties of locomotor gaits.Trot and bound are identified as attractor gaits,walk as a semi-attractor gait,and gallop as a transitional gait,with predictable transitions between these gaits.The model suggests that cervical-lumbar circuits are asymmetrically recruited during quadrupedal locomotion,thereby providing new insights into the neural control of speed-dependent gait expression.展开更多
Presently,we develop a simplified corticothalamic(SCT)model and propose a single-pulse alternately resetting stimulation(SARS)with sequentially applying anodic(A,“+”)or cathodic(C,“−”)phase pulses to the thalamic ...Presently,we develop a simplified corticothalamic(SCT)model and propose a single-pulse alternately resetting stimulation(SARS)with sequentially applying anodic(A,“+”)or cathodic(C,“−”)phase pulses to the thalamic reticular(RE)nuclei,thalamus-cortex(TC)relay nuclei,and cortical excitatory(EX)neurons,respectively.Abatement effects of ACC-SARS of RE,TC,and EX for the 2 Hz-4 Hz spike and wave discharges(SWD)of absence seizures are then concerned.The m∶n on-off ACC-SARS protocol is shown to effectively reduce the SWD with the least current consumption.In particular,when its frequency is out of the 2 Hz-4 Hz SWD dominant rhythm,the desired seizure abatements can be obtained,which can be further improved by our proposed directional steering(DS)stimulation.The dynamical explanations for the SARS induced seizure abatements are lastly given by calculating the averaged mean firing rate(AMFR)of neurons and triggering averaged mean firing rates(TAMFRs)of 2 Hz-4 Hz SWD.展开更多
Biophysical computational models are complementary to experiments and theories,providing powerful tools for the study of neurological diseases.The focus of this review is the dynamic modeling and control strategies of...Biophysical computational models are complementary to experiments and theories,providing powerful tools for the study of neurological diseases.The focus of this review is the dynamic modeling and control strategies of Parkinson’s disease(PD).In previous studies,the development of parkinsonian network dynamics modeling has made great progress.Modeling mainly focuses on the cortex-thalamus-basal ganglia(CTBG)circuit and its sub-circuits,which helps to explore the dynamic behavior of the parkinsonian network,such as synchronization.Deep brain stimulation(DBS)is an effective strategy for the treatment of PD.At present,many studies are based on the side effects of the DBS.However,the translation from modeling results to clinical disease mitigation therapy still faces huge challenges.Here,we introduce the progress of DBS improvement.Its specific purpose is to develop novel DBS treatment methods,optimize the treatment effect of DBS for each patient,and focus on the study in closed-loop DBS.Our goal is to review the inspiration and insights gained by combining the system theory with these computational models to analyze neurodynamics and optimize DBS treatment.展开更多
Chua＇s circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua＇s circuit system with the smooth deg...Chua＇s circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua＇s circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the su- percritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous （PWSC） systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. There- fore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features.展开更多
This paper proposes a distributed control method based on the differential flatness(DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the co...This paper proposes a distributed control method based on the differential flatness(DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the control objective. The DF mapping refers to the fact that the system state and input of each robot can be derived algebraically from the flat outputs of the leaders and the cooperative errors and their finite order derivatives. Based on the proposed swarm DF mapping, a distributed controller is designed. The distributed implementation of swarm DF mapping is achieved through observer design. The effectiveness of the proposed method is validated through a numerical simulation of quadrotor swarm synchronization.展开更多
Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation betw...Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation between two species as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits.A stochastic fluctuation of the positive feedback strength is introduced in a bistable interval of the feedback strength,and bistability appears for the moderate feedback strength at a certain noise level.Stability analysis based on the potential energy landscape is further utilized to explore the noise-induced switching behavior of two stable steady states.展开更多
We investigate synchronization of Hindmarsh Ftose neurons with gap junctions under the control of a pacemaker. In a ring Hindmarsh-Rose neuronal network, the coupled neurons with the pacemaker can occur in synchroniza...We investigate synchronization of Hindmarsh Ftose neurons with gap junctions under the control of a pacemaker. In a ring Hindmarsh-Rose neuronal network, the coupled neurons with the pacemaker can occur in synchronization more easily than those without the pacemaker. Furthermore, the pacemaker can induce phase synchronization or nearly-complete synchronization of nonidentical neurons. This synchronization can occur more easily when time delay is considered. Theses results can be helpful to understand the activities of the real neuronal system.展开更多
In this paper,we investigate the evolution of spatiotemporal patterns and synchronization transitions in dependence on the information transmission delay and ion channel blocking in scale-free neuronal networks.As the...In this paper,we investigate the evolution of spatiotemporal patterns and synchronization transitions in dependence on the information transmission delay and ion channel blocking in scale-free neuronal networks.As the underlying model of neuronal dynamics,we use the Hodgkin-Huxley equations incorporating channel blocking and intrinsic noise.It is shown that delays play a significant yet subtle role in shaping the dynamics of neuronal networks.In particular,regions of irregular and regular propagating excitatory fronts related to the synchronization transitions appear intermittently as the delay increases.Moreover,the fraction of working sodium and potassium ion channels can also have a significant impact on the spatiotemporal dynamics of neuronal networks.As the fraction of blocked sodium channels increases,the frequency of excitatory events decreases,which in turn manifests as an increase in the neuronal synchrony that,however,is dysfunctional due to the virtual absence of large-amplitude excitations.Expectedly,we also show that larger coupling strengths improve synchronization irrespective of the information transmission delay and channel blocking.The presented results are also robust against the variation of the network size,thus providing insights that could facilitate understanding of the joint impact of ion channel blocking and information transmission delay on the spatiotemporal dynamics of neuronal networks.展开更多
Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and paramet...Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency （wave number） of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.展开更多
We investigate asymptotical stabilization for a class of chaotic systems by means of quantization measurements of states.The quantizer adopted in this paper takes finite many values.In particular,one zoomer is placed ...We investigate asymptotical stabilization for a class of chaotic systems by means of quantization measurements of states.The quantizer adopted in this paper takes finite many values.In particular,one zoomer is placed at the input terminal of the quantizer,and another zoomer is located at the output terminal of the quantizer.The zoomers possess a common adjustable time-varying parameter.By using the adaptive laws for the time-varying parameter and estimating boundary error of values of quantization,the stabilization feedback controller with the quantized state measurements is proposed for a class of chaotic systems.Finally,some numerical examples are given to demonstrate the validity of the proposed methods.展开更多
It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its...It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris-Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.展开更多
The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed. For bilateral constraints, frictional forces and their impulses contain the ...The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed. For bilateral constraints, frictional forces and their impulses contain the products of the filled-in relay function induced by Coulomb friction and the absolute values of normal constraint reactions. With the time-stepping impulse-velocity scheme, the measure differential equations are discretized. The equations of horizontal linear complementarity problems （HLCPs）, which are used to compute the impulses, are constructed by decomposing the absolute function and the filled-in relay function. These HLCP equations degenerate into equations of LCPs for frictional unilateral constraints, or HLCPs for frictional bilateral constraints. Finally, a numerical simulation for multibody systems with both unilateral and bilateral constraints is presented.展开更多
We examine how noise interacts with encoding mechanisms of neuronal stimulus in a cold receptor. From ISI series and bifurcation diagrams it is shown that there are considerable differences in interval distributions a...We examine how noise interacts with encoding mechanisms of neuronal stimulus in a cold receptor. From ISI series and bifurcation diagrams it is shown that there are considerable differences in interval distributions and impulse patterns caused by purely deterministic simulations and noisy simulations. The ISI-distance can be used as an effective and powerful way to measure the noise effects on spike trains of the cold receptor quantitatively. It is also found that spike trains observed in cold receptors can be more strongly affected by noise for low temperatures than for high temperatures in some aspects; meanwhile, the spike train has greater variability with increasing noise intensity.展开更多
We numerically study how non-Gaussian colored noise affects the spatial coherence of a Hodgkin-Huxley neuronal network. From the simulation results, we find that there exists some intermediate noise intensities, corre...We numerically study how non-Gaussian colored noise affects the spatial coherence of a Hodgkin-Huxley neuronal network. From the simulation results, we find that there exists some intermediate noise intensities, correlation time of the colored noise, and the deviation from Gaussian colored noise, for which an ordered pattern with a characteristic spatial frequency of the system comes forth in a resonant manner. Namely, under certain conditions, spatial coherence of the studied neuronal network can be optimized by the non-Gaussian colored noise, which indicates the occurrence of spatial coherence resonance.展开更多
Sloshing-induced force and moment may affect the dynamic property of the liquid-contained system.Analytically presented linear Stokes-Joukowski potentials of fluid are usually needed for analytical study of sloshing i...Sloshing-induced force and moment may affect the dynamic property of the liquid-contained system.Analytically presented linear Stokes-Joukowski potentials of fluid are usually needed for analytical study of sloshing in liquid-filled tank under rotational(e.g.,pitching)excitations.To obtain the analytically approximate linear Stokes-Joukowski potentials of fluid in the rigid baffled tanks,a variational domain-decomposition scheme is proposed.This scheme includes three steps:(i)dividing the hydrostatic baffled fluid domain into simple sub-domains based on the positions of the baffles(i.e.,using the baffle as part of the boundaries of the sub-domain)by introducing artificial interfaces and densities of fluids in the different sub-domains or auxiliary normal fluid velocity functions on the artificial interfaces;(ii)expressing the solution for linear Stokes-Joukowski potential of each sub-domain as a linear combination of a class of harmonic functions with undetermined coefficients,and expressing the auxiliary normal fluid velocity functions on the artificial in terfaces as Fourier-type series with undetermined coefficients;(iii)solving the undetermined coefficients by the Trefftz method and the proposed variational formulations.The obtained semi-analytical linear Stokes-Joukowski potential agrees well with that published in literature or given by finite element method(FEM),and its applicability to study nonlinear sloshing problem is verified by applying it to a two-dimensional partially fluid-filled rectangular tank with a T-shaped baffle under pitching excitation.The present semi-analytical result is compared with that given by computational fluid dynamics(CFD)software or literature.展开更多
We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of nu...We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.展开更多
Taking account of the Ca2＋-activated degradation of inositol trisphosphate （IP3）, a one pool model of cytosolic calcium oscillation is considered to investigate the effect of the calcium pump on the Ca2＋ bursting ...Taking account of the Ca2＋-activated degradation of inositol trisphosphate （IP3）, a one pool model of cytosolic calcium oscillation is considered to investigate the effect of the calcium pump on the Ca2＋ bursting oscillation behavior. In order to give the oscillation domain, a two-parameter bifurcation analysis of the fast subsystem is performed in the parameter plane. Different types of bursting are presented with the variation of the pump parameter, and fast-slow dynamics is used to analyze the types and generation mechanisms of the bursting oscillations. The results are instructive for understanding the role of the calcium pump played in complex intracellular calcium activities.展开更多
This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose(HR)neuronal model with the time-delayed feedback control.By stability and bifurcation analysis,we find that the excitable neuron can em...This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose(HR)neuronal model with the time-delayed feedback control.By stability and bifurcation analysis,we find that the excitable neuron can emit spikes via the subcritical Hopf bifurcation,and exhibits periodic or chaotic spiking/bursting behaviors with the increase of external current.For the purpose of control of chaos,we adopt the time-delayed feedback control,and convert chaos control to the Hopf bifurcation of the delayed feedback system.Then the analytical conditions under which the Hopf bifurcation occurs are given with an explicit formula.Based on this,we show the Hopf bifurcation curves in the two-parameter plane.Finally,some numerical simulations are carried out to support the theoretical results.It is shown that by appropriate choice of feedback gain and time delay,the chaotic orbit can be controlled to be stable.The adopted method in this paper is general and can be applied to other neuronal models.It may help us better understand the bifurcation mechanisms of neural behaviors.展开更多
In this paper,the problem of adaptive finite time formation control is investigated for double integrator multi-agent systems with uncertainties.Firstly,considering the multi-agent systems with uncertain dynamic refer...In this paper,the problem of adaptive finite time formation control is investigated for double integrator multi-agent systems with uncertainties.Firstly,considering the multi-agent systems with uncertain dynamic reference and external bounded disturbance,a distributed adaptive estimator control algorithm is designed to realize formation tracking control in finite-time.It is important that the collision avoidance and maintaining connectivity of the multi-agent systems are realized by constructing an effective potential function based on distance constraints.On the other hand,the problem of formation production control for the double integrator systems is discussed with desired formation shape in finite-time.Achieving four control objectives is the main contributions in all the phases,including the estimation of uncertainties,collision avoidance,connectivity maintenance,and finite-time convergence.Finally,an application example of the formation production control is presented to verify accuracy of the proposed theoretical method.展开更多
Based on the topological characteristics of small-world networks,a nonlinear sliding mode controller is designed to minimize the effects of internal parameter uncertainties.To qualify the effects of uncertain paramete...Based on the topological characteristics of small-world networks,a nonlinear sliding mode controller is designed to minimize the effects of internal parameter uncertainties.To qualify the effects of uncertain parameters in the response networks,some effective recognition rates are designed so as to achieve a steady value in the extremely fast simulation time period.Meanwhile,the Fisher-Kolmogorov and Burgers spatiotemporal chaotic systems are selected as the network nodes for constructing a drive and a response network,respectively.The simulation results confirm that the developed sliding mode could realize the effective synchronization problem between the spatiotemporal networks,and the outer synchronization is still achieved timely even when the connection probability of the small-world networks changes.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12272092 and 12332004)。
文摘In quadrupeds,the cervical and lumbar circuits work together to achieve the speed-dependent gait expression.While most studies have focused on how local lumbar circuits regulate limb coordination and gaits,relatively few studies are known about cervical circuits and even less about locomotor gaits.We use the previously published models by Danner et al.(DANNER,S.M.,SHEVTSOVA,N.A.,FRIGON,A.,and RYBAK,I.A.Computational modeling of spinal circuits controlling limb coordination and gaits in quadrupeds.e Life,6,e31050(2017))as a basis,and modify it by proposing an asymmetric organization of cervical and lumbar circuits.First,the model reproduces the typical speed-dependent gait expression in mice and more biologically appropriate locomotor parameters,including the gallop gait,locomotor frequencies,and limb coordination of the forelimbs.Then,the model replicates the locomotor features regulated by the M-current.The walk frequency increases with the M-current without affecting the interlimb coordination or gaits.Furthermore,the model reveals the interaction mechanism between the brainstem drive and ionic currents in regulating quadrupedal locomotion.Finally,the model demonstrates the dynamical properties of locomotor gaits.Trot and bound are identified as attractor gaits,walk as a semi-attractor gait,and gallop as a transitional gait,with predictable transitions between these gaits.The model suggests that cervical-lumbar circuits are asymmetrically recruited during quadrupedal locomotion,thereby providing new insights into the neural control of speed-dependent gait expression.
基金Project supported by the National Natural Science Foundation of China(Nos.11702018,11932003,and 11672074)。
文摘Presently,we develop a simplified corticothalamic(SCT)model and propose a single-pulse alternately resetting stimulation(SARS)with sequentially applying anodic(A,“+”)or cathodic(C,“−”)phase pulses to the thalamic reticular(RE)nuclei,thalamus-cortex(TC)relay nuclei,and cortical excitatory(EX)neurons,respectively.Abatement effects of ACC-SARS of RE,TC,and EX for the 2 Hz-4 Hz spike and wave discharges(SWD)of absence seizures are then concerned.The m∶n on-off ACC-SARS protocol is shown to effectively reduce the SWD with the least current consumption.In particular,when its frequency is out of the 2 Hz-4 Hz SWD dominant rhythm,the desired seizure abatements can be obtained,which can be further improved by our proposed directional steering(DS)stimulation.The dynamical explanations for the SARS induced seizure abatements are lastly given by calculating the averaged mean firing rate(AMFR)of neurons and triggering averaged mean firing rates(TAMFRs)of 2 Hz-4 Hz SWD.
基金Project supported by the National Natural Science Foundation of China(Nos.11932003 and 11772019)。
文摘Biophysical computational models are complementary to experiments and theories,providing powerful tools for the study of neurological diseases.The focus of this review is the dynamic modeling and control strategies of Parkinson’s disease(PD).In previous studies,the development of parkinsonian network dynamics modeling has made great progress.Modeling mainly focuses on the cortex-thalamus-basal ganglia(CTBG)circuit and its sub-circuits,which helps to explore the dynamic behavior of the parkinsonian network,such as synchronization.Deep brain stimulation(DBS)is an effective strategy for the treatment of PD.At present,many studies are based on the side effects of the DBS.However,the translation from modeling results to clinical disease mitigation therapy still faces huge challenges.Here,we introduce the progress of DBS improvement.Its specific purpose is to develop novel DBS treatment methods,optimize the treatment effect of DBS for each patient,and focus on the study in closed-loop DBS.Our goal is to review the inspiration and insights gained by combining the system theory with these computational models to analyze neurodynamics and optimize DBS treatment.
基金supported by the National Natural Science Foundation of China(Nos.U1204106,11372282,11272024,and 11371046)the National Basic Research Program of China(973 Program)(Nos.2012CB821200 and 2012CB821202)
文摘Chua＇s circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua＇s circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the su- percritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous （PWSC） systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. There- fore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features.
基金Project supported by the National Natural Science Foundation of China (Nos. 62373025, 12332004,62003013, and 11932003)。
文摘This paper proposes a distributed control method based on the differential flatness(DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the control objective. The DF mapping refers to the fact that the system state and input of each robot can be derived algebraically from the flat outputs of the leaders and the cooperative errors and their finite order derivatives. Based on the proposed swarm DF mapping, a distributed controller is designed. The distributed implementation of swarm DF mapping is achieved through observer design. The effectiveness of the proposed method is validated through a numerical simulation of quadrotor swarm synchronization.
基金supported by the National Natural Science Foundation of China(Grants 11372017,11272024,and 11371046)the General Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant NJZY14130)
文摘Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation between two species as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits.A stochastic fluctuation of the positive feedback strength is introduced in a bistable interval of the feedback strength,and bistability appears for the moderate feedback strength at a certain noise level.Stability analysis based on the potential energy landscape is further utilized to explore the noise-induced switching behavior of two stable steady states.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10872014, 10802012 and 11072013.
文摘We investigate synchronization of Hindmarsh Ftose neurons with gap junctions under the control of a pacemaker. In a ring Hindmarsh-Rose neuronal network, the coupled neurons with the pacemaker can occur in synchronization more easily than those without the pacemaker. Furthermore, the pacemaker can induce phase synchronization or nearly-complete synchronization of nonidentical neurons. This synchronization can occur more easily when time delay is considered. Theses results can be helpful to understand the activities of the real neuronal system.
基金supported by the National Natural Science Foundation of China(11172017 and 10972001)the Fujian Natural Science Foundation of China(2009J05004)a Key Project of Fujian Provincial Universities(Information Technology Research Based on Mathematics)
文摘In this paper,we investigate the evolution of spatiotemporal patterns and synchronization transitions in dependence on the information transmission delay and ion channel blocking in scale-free neuronal networks.As the underlying model of neuronal dynamics,we use the Hodgkin-Huxley equations incorporating channel blocking and intrinsic noise.It is shown that delays play a significant yet subtle role in shaping the dynamics of neuronal networks.In particular,regions of irregular and regular propagating excitatory fronts related to the synchronization transitions appear intermittently as the delay increases.Moreover,the fraction of working sodium and potassium ion channels can also have a significant impact on the spatiotemporal dynamics of neuronal networks.As the fraction of blocked sodium channels increases,the frequency of excitatory events decreases,which in turn manifests as an increase in the neuronal synchrony that,however,is dysfunctional due to the virtual absence of large-amplitude excitations.Expectedly,we also show that larger coupling strengths improve synchronization irrespective of the information transmission delay and channel blocking.The presented results are also robust against the variation of the network size,thus providing insights that could facilitate understanding of the joint impact of ion channel blocking and information transmission delay on the spatiotemporal dynamics of neuronal networks.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872014)
文摘Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency （wave number） of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.
基金Supported by the National Science Foundation of China under Grant No.11172017the Guangdong Natural Science Foundation under Grant No.8151009001000061Natural Science Joint Research Program Foundation of Guangdong Province under Grant No.8351009001000002
文摘We investigate asymptotical stabilization for a class of chaotic systems by means of quantization measurements of states.The quantizer adopted in this paper takes finite many values.In particular,one zoomer is placed at the input terminal of the quantizer,and another zoomer is located at the output terminal of the quantizer.The zoomers possess a common adjustable time-varying parameter.By using the adaptive laws for the time-varying parameter and estimating boundary error of values of quantization,the stabilization feedback controller with the quantized state measurements is proposed for a class of chaotic systems.Finally,some numerical examples are given to demonstrate the validity of the proposed methods.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10872014 and 10802012)the Development Foundation of Science of Nanjing University of Science and Technology (Grant No.XKF09036)
文摘It is crucially important to study different synchronous regimes in coupled neurons because different regimes may correspond to different cognitive and pathological states. In this paper, phase synchronization and its transitions are discussed by means of theoretical and numerical analyses. In two coupled modified Morris-Lecar neurons with a gap junction, we show that the occurrence of phase synchronization can be investigated from the dynamics of phase equation, and the analytical synchronization condition is derived. By defining the phase of spike and burst, the transitions from burst synchronization to spike synchronization and then toward nearly complete synchronization can be identified by bifurcation diagrams, the mean frequency difference and time series of neurons. The simulation results suggest that the synchronization of bursting activity is a multi-time-scale phenomenon and the phase synchronization deduced by the phase equation is actually spike synchronization.
基金supported by the National Natural Science Foundation of China (10672007)
文摘The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed. For bilateral constraints, frictional forces and their impulses contain the products of the filled-in relay function induced by Coulomb friction and the absolute values of normal constraint reactions. With the time-stepping impulse-velocity scheme, the measure differential equations are discretized. The equations of horizontal linear complementarity problems （HLCPs）, which are used to compute the impulses, are constructed by decomposing the absolute function and the filled-in relay function. These HLCP equations degenerate into equations of LCPs for frictional unilateral constraints, or HLCPs for frictional bilateral constraints. Finally, a numerical simulation for multibody systems with both unilateral and bilateral constraints is presented.
基金Supported by the National Natural Science Foundation of China under Grant No 10872014.
文摘We examine how noise interacts with encoding mechanisms of neuronal stimulus in a cold receptor. From ISI series and bifurcation diagrams it is shown that there are considerable differences in interval distributions and impulse patterns caused by purely deterministic simulations and noisy simulations. The ISI-distance can be used as an effective and powerful way to measure the noise effects on spike trains of the cold receptor quantitatively. It is also found that spike trains observed in cold receptors can be more strongly affected by noise for low temperatures than for high temperatures in some aspects; meanwhile, the spike train has greater variability with increasing noise intensity.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11102094 and 11272024, and the Fundamental Research Funds for the Central University under Grant No 2013RC0904.
文摘We numerically study how non-Gaussian colored noise affects the spatial coherence of a Hodgkin-Huxley neuronal network. From the simulation results, we find that there exists some intermediate noise intensities, correlation time of the colored noise, and the deviation from Gaussian colored noise, for which an ordered pattern with a characteristic spatial frequency of the system comes forth in a resonant manner. Namely, under certain conditions, spatial coherence of the studied neuronal network can be optimized by the non-Gaussian colored noise, which indicates the occurrence of spatial coherence resonance.
基金the National Natural Science Foundation of China(Grant Nos.11572018 and 11772020).
文摘Sloshing-induced force and moment may affect the dynamic property of the liquid-contained system.Analytically presented linear Stokes-Joukowski potentials of fluid are usually needed for analytical study of sloshing in liquid-filled tank under rotational(e.g.,pitching)excitations.To obtain the analytically approximate linear Stokes-Joukowski potentials of fluid in the rigid baffled tanks,a variational domain-decomposition scheme is proposed.This scheme includes three steps:(i)dividing the hydrostatic baffled fluid domain into simple sub-domains based on the positions of the baffles(i.e.,using the baffle as part of the boundaries of the sub-domain)by introducing artificial interfaces and densities of fluids in the different sub-domains or auxiliary normal fluid velocity functions on the artificial interfaces;(ii)expressing the solution for linear Stokes-Joukowski potential of each sub-domain as a linear combination of a class of harmonic functions with undetermined coefficients,and expressing the auxiliary normal fluid velocity functions on the artificial in terfaces as Fourier-type series with undetermined coefficients;(iii)solving the undetermined coefficients by the Trefftz method and the proposed variational formulations.The obtained semi-analytical linear Stokes-Joukowski potential agrees well with that published in literature or given by finite element method(FEM),and its applicability to study nonlinear sloshing problem is verified by applying it to a two-dimensional partially fluid-filled rectangular tank with a T-shaped baffle under pitching excitation.The present semi-analytical result is compared with that given by computational fluid dynamics(CFD)software or literature.
基金Supported by National Natural Science Foundation under Grant No.11002073the Fundamental Research Funds for the Central Universities under Grant No.2011RC0702
文摘We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.
基金Supported by the National Natural Science Foundation of China under Grant No 10872014.
文摘Taking account of the Ca2＋-activated degradation of inositol trisphosphate （IP3）, a one pool model of cytosolic calcium oscillation is considered to investigate the effect of the calcium pump on the Ca2＋ bursting oscillation behavior. In order to give the oscillation domain, a two-parameter bifurcation analysis of the fast subsystem is performed in the parameter plane. Different types of bursting are presented with the variation of the pump parameter, and fast-slow dynamics is used to analyze the types and generation mechanisms of the bursting oscillations. The results are instructive for understanding the role of the calcium pump played in complex intracellular calcium activities.
基金supported by the National Natural Science Foundation of China(Grant Nos.110020731117201711102041)
文摘This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose(HR)neuronal model with the time-delayed feedback control.By stability and bifurcation analysis,we find that the excitable neuron can emit spikes via the subcritical Hopf bifurcation,and exhibits periodic or chaotic spiking/bursting behaviors with the increase of external current.For the purpose of control of chaos,we adopt the time-delayed feedback control,and convert chaos control to the Hopf bifurcation of the delayed feedback system.Then the analytical conditions under which the Hopf bifurcation occurs are given with an explicit formula.Based on this,we show the Hopf bifurcation curves in the two-parameter plane.Finally,some numerical simulations are carried out to support the theoretical results.It is shown that by appropriate choice of feedback gain and time delay,the chaotic orbit can be controlled to be stable.The adopted method in this paper is general and can be applied to other neuronal models.It may help us better understand the bifurcation mechanisms of neural behaviors.
基金work was supported by the National Natural Science Foundation of China(Grant Nos.11962019,11932003,11602115,11602146 and 11802006)the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT-17-B33)+1 种基金the Beijing Natural Science Foundation(Grant No.1194024)and the Fundamental Research Funds for the Central。
文摘In this paper,the problem of adaptive finite time formation control is investigated for double integrator multi-agent systems with uncertainties.Firstly,considering the multi-agent systems with uncertain dynamic reference and external bounded disturbance,a distributed adaptive estimator control algorithm is designed to realize formation tracking control in finite-time.It is important that the collision avoidance and maintaining connectivity of the multi-agent systems are realized by constructing an effective potential function based on distance constraints.On the other hand,the problem of formation production control for the double integrator systems is discussed with desired formation shape in finite-time.Achieving four control objectives is the main contributions in all the phases,including the estimation of uncertainties,collision avoidance,connectivity maintenance,and finite-time convergence.Finally,an application example of the formation production control is presented to verify accuracy of the proposed theoretical method.
基金Project supported by the National Natural Science Foundation of China(Nos.11602146,11872304,and 11962019)the Science Foundation of Shanghai(No.18ZR1438200)and the Chen Guang Project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation(No.16CG65)。
文摘Based on the topological characteristics of small-world networks,a nonlinear sliding mode controller is designed to minimize the effects of internal parameter uncertainties.To qualify the effects of uncertain parameters in the response networks,some effective recognition rates are designed so as to achieve a steady value in the extremely fast simulation time period.Meanwhile,the Fisher-Kolmogorov and Burgers spatiotemporal chaotic systems are selected as the network nodes for constructing a drive and a response network,respectively.The simulation results confirm that the developed sliding mode could realize the effective synchronization problem between the spatiotemporal networks,and the outer synchronization is still achieved timely even when the connection probability of the small-world networks changes.
