Spiral waves,as a typical self-organized structure with chiral characteristics,are widely found in excitable media such as cardiac tissues,chemical reactions,and neural networks.Based on the Fitz Hugh–Nagumo model,we...Spiral waves,as a typical self-organized structure with chiral characteristics,are widely found in excitable media such as cardiac tissues,chemical reactions,and neural networks.Based on the Fitz Hugh–Nagumo model,we investigated the mechanisms underlying the effects of direct current electric fields(DCEF),alternating current electric fields(ACEF),and polarized electric fields(PEF)on the interaction and annihilation processes of counter-rotating spiral waves.We found that in a direct current electric field,the drift direction of the spiral wave is determined jointly by its chirality and the electric field direction,which allows selective attraction or repulsion.In an alternating current electric field,the annihilation behavior of spiral waves can be influenced by the phase and intensity of the electric field,where a specific range of parameters induces resonance drift and eventual annihilation.On the other hand,the polarized electric field exhibits a more complex modulation capability on spiral waves:the trajectory and annihilation efficiency of spiral waves can be regulated by both the intensity and phase of the polarized electric field.These results reveal the potential feasibility of regulating multichiral spiral waves through multiple electric fields,providing theoretical insight for the control of spiral waves in relevant systems.展开更多
In this paper, an intermittent local electric shock scheme is proposed to suppress stable spiral waves in the Barkley model by a weak electric shock （about 0.4 to 0.7） imposed on a random selected n × n grids ...In this paper, an intermittent local electric shock scheme is proposed to suppress stable spiral waves in the Barkley model by a weak electric shock （about 0.4 to 0.7） imposed on a random selected n × n grids （n =1 - 5, compared with the original 256×256 lattice） and monitored synchronically the evolutions of the activator on the grids as the sampled signal of the activator steps out a given threshold （i.e., the electric shock works on the n ~ n grids if the activator u ≤ 0.4 or u ≥ 0.8）. The numerical simulations show that a breakup of spiral is observed in the media state evolution to finally obtain homogeneous states if the electric shock with appropriate intensity is imposed.展开更多
We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coup...We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coupling strength, the synchronization is broken down. With the further increase of the coupling strength, complete synchronization and phase synchronization occur again. We also found that the inhomogeneity in excitable systems is helpful to the synchronization.展开更多
Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,...Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,spiral waves and spatiotemporal chaos can be eliminated by the trains for some certain excitation periods. Obvious resonant behavior can be observed from the relation between the periods of the trains and excitation ones. The method is against noise.展开更多
A method to eliminate spiral waves and spatiotemporal chaos by using the synchronization transmission technology of network signals is proposed in this paper. The character of the spiral waves and the spatiotemporal c...A method to eliminate spiral waves and spatiotemporal chaos by using the synchronization transmission technology of network signals is proposed in this paper. The character of the spiral waves and the spatiotemporal chaos in the Fitzhugh-Nagumo model is presented. The network error evolution equation with spatiotemporal variables and the corresponding eigenvalue equation are determined based on the stability theory, and the global synchronization condition is obtained. Simulations are made in a complex network with Fitzhugh-Nagumo models as the nodes to verify the effectiveness of the synchronization transmission principle of the network signal.展开更多
In this paper, a close-loop feedback control is imposed locally on the Fitzhugh-Nagumo （FHN） system to suppress the stable spirals and spatiotemporal chaos according to the principle of self-adaptive coupling intera...In this paper, a close-loop feedback control is imposed locally on the Fitzhugh-Nagumo （FHN） system to suppress the stable spirals and spatiotemporal chaos according to the principle of self-adaptive coupling interaction. The simulation results show that an expanding target wave is stimulated by the spiral waves under dynamic control period when a local area. of 5 × 5 grids is controlled, or the spiral tip is driven to the board of the system, It is also found that the spatiotemporal chaos can be suppressed to get a stable homogeneous state within 50 time units as two local grids are controlled mutually. The mechanism of the scheme is briefly discussed.展开更多
The influence of long-range links on spiral waves in an excitable medium has been investigated. Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connecti...The influence of long-range links on spiral waves in an excitable medium has been investigated. Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connection probability P. Spiral waves with few perturbations, broken spiral waves, pseudo spiral turbulence, synchronous oscillations, and homogeneous rest state are discovered under different network structures. Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns. The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state. Finally, we use long-range links to successfully control spiral waves and spiral turbulence.展开更多
Diversity in the neurons and noise are inevitable in the real neuronal network.In this paper,parameter diversity induced spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network wit...Diversity in the neurons and noise are inevitable in the real neuronal network.In this paper,parameter diversity induced spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network without or with noise are simulated.The relationship between the multiple resonances and the multiple transitions between patterns of spiral waves are identified.The coherence degrees induced by the diversity are suppressed when noise is introduced and noise density is increased.The results suggest that natural nervous system might profit from both parameter diversity and noise,provided a possible approach to control formation and transition of spiral wave by the cooperation between the diversity and noise.展开更多
Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris-Lecar neurons are studied.Each neuron is at resting state near a saddle-node bif...Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris-Lecar neurons are studied.Each neuron is at resting state near a saddle-node bifurcation on invariant circle,coupled to its nearest neighbors by electronic coupling.Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity.By calculating spatial structure function and signal-to-noise ratio(SNR),it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered,respectively.SNR manifest multiple local maximal peaks,indicating that the colored noise can induce multiple spatial coherence resonances.The maximal SNR values decrease as the correlation time of the noise increases.These results not only provide an example of multiple resonances,but also show that Gaussian colored noise play constructive roles in neuronal network.展开更多
In this paper, we consider a model system with two identical time-delayed coupled layers. Synchronization and anti-phase synchronization are exhibited in the reactive system without diffusion term. New segmented spira...In this paper, we consider a model system with two identical time-delayed coupled layers. Synchronization and anti-phase synchronization are exhibited in the reactive system without diffusion term. New segmented spiral waves, which are constituted by many thin trips, are found in each layer of two identical time-delayed coupled layers, and are different from the segmented spiral waves in a water-in-oil aerosol sodium bis（2-ethylhexyl） sulfosuccinate （AOT） microemulsion （ME） （BZ-AOT system）, which consists of many small segments. ＂Anti-phase spiral wave synchronization＂ can be realized between the first layer and the second one. For different excitable parameters, we also give the minimum values of the coupling strength to generate segmented spiral waves and the tip orbits of spiral waves in the whole bilayer.展开更多
The domain size of spiral waves is an important issue in studies of two-dimensional （2D） spatiotemporal patterns. In this work, we use the 2D complex Ginzburg-Landau equation （CGLE） as our model and find that an i...The domain size of spiral waves is an important issue in studies of two-dimensional （2D） spatiotemporal patterns. In this work, we use the 2D complex Ginzburg-Landau equation （CGLE） as our model and find that an initially big spiral can successfully transfer to several small spirals by applying a pulse array method. The impacts of several important factors, such as array density, controlling intensity and pulsing time, are investigated. This control approach may be useful for the control of 2D spatiotemporal patterns and has potential applications in the control of some realistic systems, such as meteorological and cardiac systems.展开更多
Based on the Tang-Othmer Ca^2＋ model, the drift behavior of intracellular Ca^2＋ spiral waves under the influence of weak electric field is investigated. Numerical results show that the dependence of drift velocity o...Based on the Tang-Othmer Ca^2＋ model, the drift behavior of intracellular Ca^2＋ spiral waves under the influence of weak electric field is investigated. Numerical results show that the dependence of drift velocity of the spiral tip on dc electric field is similar to experimental observations in BZ system. When an ac electric field is applied, interesting resonant-drift phenomenon is observed with ω=2ω0. All results can be explained analytically using a proximate method.展开更多
Cellular aging can result in deterioration of electrical coupling, the extension of the action potential duration, and lower excitability of the cell. Those factors are introduced into the Greenberg–Hastings cellular...Cellular aging can result in deterioration of electrical coupling, the extension of the action potential duration, and lower excitability of the cell. Those factors are introduced into the Greenberg–Hastings cellular automaton model and the effects of the cellular aging on the dynamics of spiral waves are studied. The numerical results show that a 50% reduction of the coupling strength of aging cells has a little influence on spiral waves. If the coupling strength of aging cells equals zero, the ability for the medium to maintain spiral waves will be reduced by approximately 50% when the aging cell ratio increases from 0 to 0.5, where the reduction of cell excitability plays a major role in inducing disappearance of spiral waves. When the relevant parameters are properly chosen, the cellular aging can lead to the meandering of spiral waves,the emergence of the binary spiral waves, and even the disappearance of spiral waves via the stopping rotation or shrinkage of wave. Physical mechanisms of the above phenomena are analyzed briefly.展开更多
We numerically study the dynamics of meandering spiral waves in the excitable system subjected to a feedback signal coming from two measuring points located on a straight line together with the initial spiral core. Th...We numerically study the dynamics of meandering spiral waves in the excitable system subjected to a feedback signal coming from two measuring points located on a straight line together with the initial spiral core. The core location and size radius of the final attractors are computed, and they change with the position of the moving measuring point in a unique way. By the Fourier Spectral analysis, we find the frequency-locked behaviors different from the driving scheme of the external periodic force. It when the moving measuring point approaches closely is also found that the meandering spiral wave can be eliminated the boundary and its feedback gain is large enough. This offers an effective and convenient method for eliminating meandering spiral waves.展开更多
Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this paper spiral waves and spatiotemporal chaos are successfully eliminated by the pulse with a very specific spatiotemporal co...Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this paper spiral waves and spatiotemporal chaos are successfully eliminated by the pulse with a very specific spatiotemporal configuration. The excited position D of spiral waves or spatiotemporal chaos is first recorded at an arbitrary time （to）. When the system at the domain D enters a recovering state, the external pulse is injected into the domain. If the intensity and the working time of the pulse are appropriate, spiral waves and spatiotemporal chaos can finally be eliminated because counter-directional waves can be generated by the pulse. There are two advantages in the method. One is that the tip can be quickly eliminated together with the body of spiral wave, and the other is that the injected pulse may be weak and the duration can be very short so that the original system is nearly not affected, which is important for practical applications.展开更多
The spontaneous drift of the spiral wave in a finite domain in the complex Ginzburg Landau equation is investigated numerically. By using the interactions between the spiral wave and its images, we propose a phenomeno...The spontaneous drift of the spiral wave in a finite domain in the complex Ginzburg Landau equation is investigated numerically. By using the interactions between the spiral wave and its images, we propose a phenomenological theory to explain the observations.展开更多
The effect of physiological and pathological abnormal excitation of a myocyte on the spiral waves is investigated based on the cellular automaton model. When the excitability of the medium is high enough, the physiolo...The effect of physiological and pathological abnormal excitation of a myocyte on the spiral waves is investigated based on the cellular automaton model. When the excitability of the medium is high enough, the physiological abnormal excitation causes the spiral wave to meander irregularly and slowly. When the excitability of the medium is low enough, the physiological abnormal excitation leads to a new stable spiral wave. On the other hand, the pathological abnormal excitation destroys the spiral wave and resultsin the spatiotemporal chaos, which agrees with the clinical conclusion that the early after depolarization is the pro-arrhythmic mechanism of some anti-arrhythmic drugs. The mechanisms underlying these phenomena are analyzed.展开更多
Removal of spiral waves in cardiac muscle is necessary because of their threat to life.Common methods for this removal are to apply a local disturbance to the media,such as a periodic forcing.However,most of these met...Removal of spiral waves in cardiac muscle is necessary because of their threat to life.Common methods for this removal are to apply a local disturbance to the media,such as a periodic forcing.However,most of these methods accelerate the beating of the cardiac muscle,resulting in the aggravation of the ventricular tachycardia,which directly threatens life.In the present study,in order to clear off spiral waves,a global pulse-disturbance is applied to the media based on three models of cardiac muscle.It is found that the spiral waves are eliminated and the frequency of the cardiac muscle is decreased in a short time,and finally,the state of the medium reaches the normal oscillation,which supports a target waves.Our method sheds light on the removal of spiral waves in cardiac muscle and can prevent the ventricular tachycardia as well as the ventricular fibrillation.展开更多
A modified spatially extended Tang-Othmer Ca2＋ model is used to study intracellular Ca2＋ spiral waves numerically. It is found that, as a local stimulation, the local agonist-binding on the cell membrane, which enha...A modified spatially extended Tang-Othmer Ca2＋ model is used to study intracellular Ca2＋ spiral waves numerically. It is found that, as a local stimulation, the local agonist-binding on the cell membrane, which enhances the local concentration of the messenger molecule inositol 1,4,5-trisphosphate（IP3）, can influence the dynamics of the spiral waves. 1） Strong enough stimuli can change the spiral wave from a meandering to a rigidly rotating one. 2） On the other hand, strong enough stimuli can suppress the spiral wave from the system. It provides the theoretical clue for controlling the spiral waves by stimulating the cell membrane.展开更多
Spiral waves,whose rotation center can be regarded as a point defect,widely exist in various two-dimensional excitable systems.In this paper,by making use of Duan's topological current theory,we obtain the charge ...Spiral waves,whose rotation center can be regarded as a point defect,widely exist in various two-dimensional excitable systems.In this paper,by making use of Duan's topological current theory,we obtain the charge density of spiral waves and the topological inner structure of its topological charge.The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field.The spiral waves are found generating or annihilating at the limit points and encountering,splitting,or merging at the bifurcation points of the two-dimensional vector field.Some applications of our theory are also discussed.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12175080)by Self-Determined Research Funds of Central China Normal University from the Colleges’Basic Research and Operation of MOE(Grant No.CCNU25JC012)。
文摘Spiral waves,as a typical self-organized structure with chiral characteristics,are widely found in excitable media such as cardiac tissues,chemical reactions,and neural networks.Based on the Fitz Hugh–Nagumo model,we investigated the mechanisms underlying the effects of direct current electric fields(DCEF),alternating current electric fields(ACEF),and polarized electric fields(PEF)on the interaction and annihilation processes of counter-rotating spiral waves.We found that in a direct current electric field,the drift direction of the spiral wave is determined jointly by its chirality and the electric field direction,which allows selective attraction or repulsion.In an alternating current electric field,the annihilation behavior of spiral waves can be influenced by the phase and intensity of the electric field,where a specific range of parameters induces resonance drift and eventual annihilation.On the other hand,the polarized electric field exhibits a more complex modulation capability on spiral waves:the trajectory and annihilation efficiency of spiral waves can be regulated by both the intensity and phase of the polarized electric field.These results reveal the potential feasibility of regulating multichiral spiral waves through multiple electric fields,providing theoretical insight for the control of spiral waves in relevant systems.
文摘In this paper, an intermittent local electric shock scheme is proposed to suppress stable spiral waves in the Barkley model by a weak electric shock （about 0.4 to 0.7） imposed on a random selected n × n grids （n =1 - 5, compared with the original 256×256 lattice） and monitored synchronically the evolutions of the activator on the grids as the sampled signal of the activator steps out a given threshold （i.e., the electric shock works on the n ~ n grids if the activator u ≤ 0.4 or u ≥ 0.8）. The numerical simulations show that a breakup of spiral is observed in the media state evolution to finally obtain homogeneous states if the electric shock with appropriate intensity is imposed.
基金Project supported by the National Natural Science Foundation of China (Grant No 10305005)the Fundamental Research Fund for Physics and Mathematics of Lanzhou University, China
文摘We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coupling strength, the synchronization is broken down. With the further increase of the coupling strength, complete synchronization and phase synchronization occur again. We also found that the inhomogeneity in excitable systems is helpful to the synchronization.
基金国家重点基础研究发展计划(973计划)，中国科学院资助项目，国家自然科学基金，the Innovation Funds for Laser Technology，the Science Foundation of the Chinese Academy of Engineering Physics
文摘Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,spiral waves and spatiotemporal chaos can be eliminated by the trains for some certain excitation periods. Obvious resonant behavior can be observed from the relation between the periods of the trains and excitation ones. The method is against noise.
基金Project Supported by the National Natural Science Foundation of China (Grant No.60974004)
文摘A method to eliminate spiral waves and spatiotemporal chaos by using the synchronization transmission technology of network signals is proposed in this paper. The character of the spiral waves and the spatiotemporal chaos in the Fitzhugh-Nagumo model is presented. The network error evolution equation with spatiotemporal variables and the corresponding eigenvalue equation are determined based on the stability theory, and the global synchronization condition is obtained. Simulations are made in a complex network with Fitzhugh-Nagumo models as the nodes to verify the effectiveness of the synchronization transmission principle of the network signal.
基金The project supported partially by National Natural Science Foundation of China under Grant No. 90303010 We would like to thank H.Zhang for valuable discussions.
文摘In this paper, a close-loop feedback control is imposed locally on the Fitzhugh-Nagumo （FHN） system to suppress the stable spirals and spatiotemporal chaos according to the principle of self-adaptive coupling interaction. The simulation results show that an expanding target wave is stimulated by the spiral waves under dynamic control period when a local area. of 5 × 5 grids is controlled, or the spiral tip is driven to the board of the system, It is also found that the spatiotemporal chaos can be suppressed to get a stable homogeneous state within 50 time units as two local grids are controlled mutually. The mechanism of the scheme is briefly discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11105003)the Science Foundation of the Education Bureau of Shaanxi Province of China (Grant No. 11JK0544)
文摘The influence of long-range links on spiral waves in an excitable medium has been investigated. Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connection probability P. Spiral waves with few perturbations, broken spiral waves, pseudo spiral turbulence, synchronous oscillations, and homogeneous rest state are discovered under different network structures. Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns. The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state. Finally, we use long-range links to successfully control spiral waves and spiral turbulence.
基金Supported by National Natural Science Foundation of China under Grant Nos.11072135 and 10772101the Fundamental Research Funds for the Central Universities under Grant No.GK200902025
文摘Diversity in the neurons and noise are inevitable in the real neuronal network.In this paper,parameter diversity induced spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network without or with noise are simulated.The relationship between the multiple resonances and the multiple transitions between patterns of spiral waves are identified.The coherence degrees induced by the diversity are suppressed when noise is introduced and noise density is increased.The results suggest that natural nervous system might profit from both parameter diversity and noise,provided a possible approach to control formation and transition of spiral wave by the cooperation between the diversity and noise.
基金Supported by National Natural Science Foundation of China under Grant Nos. 11072135 and 10772101the Fundamental Research Funds for the Central Universities under Grant No. GK200902025
文摘Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris-Lecar neurons are studied.Each neuron is at resting state near a saddle-node bifurcation on invariant circle,coupled to its nearest neighbors by electronic coupling.Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity.By calculating spatial structure function and signal-to-noise ratio(SNR),it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered,respectively.SNR manifest multiple local maximal peaks,indicating that the colored noise can induce multiple spatial coherence resonances.The maximal SNR values decrease as the correlation time of the noise increases.These results not only provide an example of multiple resonances,but also show that Gaussian colored noise play constructive roles in neuronal network.
基金The project supported by National Natural Science Foundation of China under Grant No.10647127National Natural Science Foundation of China for Major Projects under Grant No.10335010the Natural Science Foundation of Hebei Province of China under Grant No.A2006000128
文摘In this paper, we consider a model system with two identical time-delayed coupled layers. Synchronization and anti-phase synchronization are exhibited in the reactive system without diffusion term. New segmented spiral waves, which are constituted by many thin trips, are found in each layer of two identical time-delayed coupled layers, and are different from the segmented spiral waves in a water-in-oil aerosol sodium bis（2-ethylhexyl） sulfosuccinate （AOT） microemulsion （ME） （BZ-AOT system）, which consists of many small segments. ＂Anti-phase spiral wave synchronization＂ can be realized between the first layer and the second one. For different excitable parameters, we also give the minimum values of the coupling strength to generate segmented spiral waves and the tip orbits of spiral waves in the whole bilayer.
文摘The domain size of spiral waves is an important issue in studies of two-dimensional （2D） spatiotemporal patterns. In this work, we use the 2D complex Ginzburg-Landau equation （CGLE） as our model and find that an initially big spiral can successfully transfer to several small spirals by applying a pulse array method. The impacts of several important factors, such as array density, controlling intensity and pulsing time, are investigated. This control approach may be useful for the control of 2D spatiotemporal patterns and has potential applications in the control of some realistic systems, such as meteorological and cardiac systems.
基金Supported by National Natural Science Foundation of China under Grant Nos.10575041 and 10747005
文摘Based on the Tang-Othmer Ca^2＋ model, the drift behavior of intracellular Ca^2＋ spiral waves under the influence of weak electric field is investigated. Numerical results show that the dependence of drift velocity of the spiral tip on dc electric field is similar to experimental observations in BZ system. When an ac electric field is applied, interesting resonant-drift phenomenon is observed with ω=2ω0. All results can be explained analytically using a proximate method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11165004 and 11365003)
文摘Cellular aging can result in deterioration of electrical coupling, the extension of the action potential duration, and lower excitability of the cell. Those factors are introduced into the Greenberg–Hastings cellular automaton model and the effects of the cellular aging on the dynamics of spiral waves are studied. The numerical results show that a 50% reduction of the coupling strength of aging cells has a little influence on spiral waves. If the coupling strength of aging cells equals zero, the ability for the medium to maintain spiral waves will be reduced by approximately 50% when the aging cell ratio increases from 0 to 0.5, where the reduction of cell excitability plays a major role in inducing disappearance of spiral waves. When the relevant parameters are properly chosen, the cellular aging can lead to the meandering of spiral waves,the emergence of the binary spiral waves, and even the disappearance of spiral waves via the stopping rotation or shrinkage of wave. Physical mechanisms of the above phenomena are analyzed briefly.
基金Supported by the National Natural Science Foundation of China under Grant No. 11005030Science Foundations of Hebei Education Department under Grant No. 2009135+1 种基金Science Foundations of Inner Mongolia Education Department under Grant No. NJ09178Science Foundation of Hebei Normal University
文摘We numerically study the dynamics of meandering spiral waves in the excitable system subjected to a feedback signal coming from two measuring points located on a straight line together with the initial spiral core. The core location and size radius of the final attractors are computed, and they change with the position of the moving measuring point in a unique way. By the Fourier Spectral analysis, we find the frequency-locked behaviors different from the driving scheme of the external periodic force. It when the moving measuring point approaches closely is also found that the meandering spiral wave can be eliminated the boundary and its feedback gain is large enough. This offers an effective and convenient method for eliminating meandering spiral waves.
基金supported by the National Natural Science Foundation of China (Grant No 10647127)the National Natural Science Foundation for Major Projects, China (Grant No 10335010)the Hebei Nature Science Foundation Project, China (Grant No A2006000128)
文摘Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this paper spiral waves and spatiotemporal chaos are successfully eliminated by the pulse with a very specific spatiotemporal configuration. The excited position D of spiral waves or spatiotemporal chaos is first recorded at an arbitrary time （to）. When the system at the domain D enters a recovering state, the external pulse is injected into the domain. If the intensity and the working time of the pulse are appropriate, spiral waves and spatiotemporal chaos can finally be eliminated because counter-directional waves can be generated by the pulse. There are two advantages in the method. One is that the tip can be quickly eliminated together with the body of spiral wave, and the other is that the injected pulse may be weak and the duration can be very short so that the original system is nearly not affected, which is important for practical applications.
基金The project supported by National Natural Science Foundation of China under Grant No. 10405004
文摘The spontaneous drift of the spiral wave in a finite domain in the complex Ginzburg Landau equation is investigated numerically. By using the interactions between the spiral wave and its images, we propose a phenomenological theory to explain the observations.
基金supported by the National Natural Science Foundation of China(Grant Nos.11365003 and 11165004)
文摘The effect of physiological and pathological abnormal excitation of a myocyte on the spiral waves is investigated based on the cellular automaton model. When the excitability of the medium is high enough, the physiological abnormal excitation causes the spiral wave to meander irregularly and slowly. When the excitability of the medium is low enough, the physiological abnormal excitation leads to a new stable spiral wave. On the other hand, the pathological abnormal excitation destroys the spiral wave and resultsin the spatiotemporal chaos, which agrees with the clinical conclusion that the early after depolarization is the pro-arrhythmic mechanism of some anti-arrhythmic drugs. The mechanisms underlying these phenomena are analyzed.
基金the National Natural Science Foundation of China(Grant Nos.11875042 and 11505114)the Shanghai project for construction of top disciplines(Grant No.USST-SYS01)。
文摘Removal of spiral waves in cardiac muscle is necessary because of their threat to life.Common methods for this removal are to apply a local disturbance to the media,such as a periodic forcing.However,most of these methods accelerate the beating of the cardiac muscle,resulting in the aggravation of the ventricular tachycardia,which directly threatens life.In the present study,in order to clear off spiral waves,a global pulse-disturbance is applied to the media based on three models of cardiac muscle.It is found that the spiral waves are eliminated and the frequency of the cardiac muscle is decreased in a short time,and finally,the state of the medium reaches the normal oscillation,which supports a target waves.Our method sheds light on the removal of spiral waves in cardiac muscle and can prevent the ventricular tachycardia as well as the ventricular fibrillation.
基金Project supported by the Xuzhou Medical College Foundation,China (Grant No. 08kj08)
文摘A modified spatially extended Tang-Othmer Ca2＋ model is used to study intracellular Ca2＋ spiral waves numerically. It is found that, as a local stimulation, the local agonist-binding on the cell membrane, which enhances the local concentration of the messenger molecule inositol 1,4,5-trisphosphate（IP3）, can influence the dynamics of the spiral waves. 1） Strong enough stimuli can change the spiral wave from a meandering to a rigidly rotating one. 2） On the other hand, strong enough stimuli can suppress the spiral wave from the system. It provides the theoretical clue for controlling the spiral waves by stimulating the cell membrane.
基金supported by National Natural Science Foundation of China and the Cuiying Programme of Lanzhou University
文摘Spiral waves,whose rotation center can be regarded as a point defect,widely exist in various two-dimensional excitable systems.In this paper,by making use of Duan's topological current theory,we obtain the charge density of spiral waves and the topological inner structure of its topological charge.The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field.The spiral waves are found generating or annihilating at the limit points and encountering,splitting,or merging at the bifurcation points of the two-dimensional vector field.Some applications of our theory are also discussed.
