This paper investigates the dynamical behaviour of the Liu system with time delayed feedback. Two typical situations are considered and the effect of time-delay parameter on the dynamics of the system is discussed. It...This paper investigates the dynamical behaviour of the Liu system with time delayed feedback. Two typical situations are considered and the effect of time-delay parameter on the dynamics of the system is discussed. It is shown that the Liu system with time delayed feedback may exhibit interesting and extremely rich dynamical behaviour. The evolution of the dynamics is shown to be complex with varying time-delay parameter. Moreover, the strange attractor like ‘wormhole＇ is detected via numerical simulations.展开更多
This paper investigates the synchronization of time delayed complex dynamical networks with periodical on-off coupling. Both the theoretical and numerical results show that, in spite of time delays and on-off coupling...This paper investigates the synchronization of time delayed complex dynamical networks with periodical on-off coupling. Both the theoretical and numerical results show that, in spite of time delays and on-off coupling, two networks may synchronize if the coupling strength and the on-off rate are large enough. It is shown that, for undirected and strongly connected networks, the upper bound of time delays for synchronization is a decreasing function of the absolute value of the minimum eigenvalue of the adjacency matrix. The theoretical analysis confirms the numerical results and provides a better understanding of the influence of time delays and on-off coupling on the synchronization transition. The influence of random delays on the synchronization is also discussed.展开更多
Biologically,because of the impact of reproduction period and nonlocal dispersal of HIV-infected cells,time delay and spatial heterogeneity should be considered.In this paper,we establish an HIV infection model with n...Biologically,because of the impact of reproduction period and nonlocal dispersal of HIV-infected cells,time delay and spatial heterogeneity should be considered.In this paper,we establish an HIV infection model with nonlocal dispersal and infection age.Moreover,applying the theory of Fourier transformation and von Foerster rule,we transform the model to an integrodifferential equation with nonlocal time delay and dispersal.The well-posedness,positivity,and boundedness of the solution for the model are studied.展开更多
In this paper, we propose a method for the projective synchronization between two different chaotic systems with variable time delays. Using active control approach, the suitable controller is constructed to make the ...In this paper, we propose a method for the projective synchronization between two different chaotic systems with variable time delays. Using active control approach, the suitable controller is constructed to make the states of two different diverse time delayed systems asymptotically synchronize up to the desired scaling factor. Based on the Lyapunov stability theory, the sufficient condition for the projective synchronization is calculated theoretically. Numerical simulations of the projective synchronization between Maekey-Glass system and Ikeda system with variable time delays are shown to validate the effectiveness of the proposed algorithm.展开更多
Time-delayed blasting is widely utilized in engineering to mitigate induced vibration hazards and enhance fragmentation.The underlying vibration reduction principle is the decrease of the charge weight per delay,while...Time-delayed blasting is widely utilized in engineering to mitigate induced vibration hazards and enhance fragmentation.The underlying vibration reduction principle is the decrease of the charge weight per delay,while the potential for further vibration reduction remains debated,largely due to unclear underlying mechanisms.In light of the popularization of electronic detonators and the representativeness of double-hole configurationsfor multiple blastholes,it is essential to investigate the vibration characteristics induced by time-delayed double blastholes.Therefore,a series of doubleborehole experimental blasts was conducted in an underground roadway to clarify the variation in vibration from single-hole to dual-hole conditions.Based on the experimental data and inherent limitations,an exact full-fieldtheoretical model was further employed to systematically analyze the effects of delay time,charge length,and borehole inclination angle on vibrations induced by various doublehole configurations.The experimental data and theoretical analysis reveal that the general scaled distance effectively predicts vibrations in delayed blasting but does not reflectvibration reduction.Increasing delay time causes fluctuatingPPVs,which stabilize slightly above single-hole PPVs as delay times exceed a certain value.The delayed blasting primarily reduces near-fieldfrequencies.Longer charge lengths in double boreholes increase PPV levels and attenuation rates within a certain length,and the vibration behavior of combined long and short charge lengths is governed by the long blasthole.Larger blasthole inclination angles enhance vibration amplitude and reduce PPV attenuation rates.Optimizing inclination angles is more critical than adjusting delay times,and parallel boreholes offer the best vibration control.展开更多
To investigate impact of time delays on the small signal stability of power systems, the least-damped eigenvalues with the smallest damping ratios have been calculated by eigen-analysis methods based on Solution Opera...To investigate impact of time delays on the small signal stability of power systems, the least-damped eigenvalues with the smallest damping ratios have been calculated by eigen-analysis methods based on Solution Operator Discretization (SOD) with Pseudo-Spectral collocation (PS) and Implicit Runge-Kutta (IRK) methods. This paper evolves SOD-PSIIRK into their partial counterparts, i.e., PSOD-PSIIRK, with greatly enhanced efficiency and reliability in analyzing large-scale time delayed power systems. Compared with SOD-PSIIRK, PSOD-PSIIRK are characterized in constructing low order discretization matrices of solution operator as well as efficiently and directly solving the embedded Matrix-Inverse-Vector Products (MIVPs). The dimensions of the discretization matrices of solution operator are largely reduced as only the retarded state variables are discretized, rather than all state variables as in SOD-PSIIRK. Meanwhile, the proposed PSOD-PSIIRK optimize the most computationally expensive operations in SOD-PSIIRK by avoiding the iterative solutions to the two embedded MIVPs. PSOD-PS/IRK directly and efficiently compute the MIVPs via factorizing the Kronecker product-like discretization matrices of the solution operator into Schur complements. The Central China-North China ultra-high-voltage power grid with 80577 state variables serves to validate the proposed PSOD-PSIIRK and shows that compared with SOD-PSIIRK, the computational time consumed by PSOD-PSIIRK is cut down by 49.96 times without loss of any accuracy.展开更多
We study the transport of overdamped Brownian particles in a symmetricaJly periodic potential in the presence of an asymmetrically ac driving force and a time-delayed feedback. It is found that for low frequencies, th...We study the transport of overdamped Brownian particles in a symmetricaJly periodic potential in the presence of an asymmetrically ac driving force and a time-delayed feedback. It is found that for low frequencies, the average velocity can be negative by changing the driving amplitude, for high frequencies, there exists an optimized driving amplitude at which the average velocity takes its maximum value. Additionally, there is a threshold value of driving amplitude below which no directed transport can be obtained for high frequencies. For the large value of the delay time, the average velocity is independent of the delay time.展开更多
With the increase of system scale, time delays have become unavoidable in nonlinear power systems, which add the complexity of system dynamics and induce chaotic oscillation and even voltage collapse events. In this p...With the increase of system scale, time delays have become unavoidable in nonlinear power systems, which add the complexity of system dynamics and induce chaotic oscillation and even voltage collapse events. In this paper, coexisting phenomenon in a fourth-order time-delayed power system is investigated for the first time with different initial conditions.With the mechanical power, generator damping factor, exciter gain, and time delay varying, the specific characteristic of the time-delayed system, including a discontinuous ＂jump＂ bifurcation behavior is analyzed by bifurcation diagrams, phase portraits, Poincar′e maps, and power spectrums. Moreover, the coexistence of two different periodic orbits and chaotic attractors with periodic orbits are observed in the power system, respectively. The production condition and existent domain of the coexistence phenomenon are helpful to avoid undesirable behavior in time-delayed power systems.展开更多
Based on the fluid flow time-delayed model proposed by Misra et al in internet congestion control, one modified time-delayed model is presented, where the influence of the communication delay on the router queue lengt...Based on the fluid flow time-delayed model proposed by Misra et al in internet congestion control, one modified time-delayed model is presented, where the influence of the communication delay on the router queue length is investigated in detail. The main advantage of the new model is that its stability domain is larger even without an extra controller. By linear stability analysis and numerical simulation, tbe effectiveness and feasibility of the novel model in internet congestion control are verified.展开更多
In this paper, the control of chemical chaotic dynamical system is investigated by time-delayed feedback control technique.The controllability and the stability of the equilibriums and local Hopf bifurcation of the sy...In this paper, the control of chemical chaotic dynamical system is investigated by time-delayed feedback control technique.The controllability and the stability of the equilibriums and local Hopf bifurcation of the system are verified. Some numerical simulations which show the effectiveness of the time-delayed feedback control method are provided.展开更多
The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of t...The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of the time delay on the Turing and Hopf instabilities near the Turing Hopf codimension-two phase space. Numerical simulations show that the transition between the Turing patterns （hexagon, stripe, and honeycomb）, the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and Hopf instabilities. Our results have shown the flexibility of the time delay on controlling the pattern formations near the Turing-Hopf codimension-two phase space.展开更多
A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model, we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed ...A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model, we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed prey to predator in the Ivlev-type functional responses. The existence and uniqueness of the positive equilibrium of the model and the stability of the equilibrium of the model are studied under various conditions. Hopf bifurcation analysis of the delayed model is provided.展开更多
Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the eff...Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the effects of noise, time delay,and their inner interactions on the network synchronization. It is found that when there exists time-delayed coupling in the network and noise diffuses through all state variables of nodes, appropriately increasing the noise intensity can effectively improve the network synchronizability;otherwise, noise can be either beneficial or harmful. For stochastic networks, large time delays will lead to desynchronization. These findings provide valuable references for designing optimal complex networks in practical applications.展开更多
We consider the robust stabilization problem for discrete-time Takagi-Sugeno （T S） fuzzy systems with time- varied delays subjected to input saturation. We design static and dynamic anti-windup fuzzy controllers to ...We consider the robust stabilization problem for discrete-time Takagi-Sugeno （T S） fuzzy systems with time- varied delays subjected to input saturation. We design static and dynamic anti-windup fuzzy controllers to ensure the convergence of all admissible initial states within the domain of attraction. Based on the project lemma and classical sector conditions, the conditions for the existence of solutions to this problem are obtained and expressed in terms of a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design approach.展开更多
The synchronization of time-delayed multi-agent networks with connected and directed topology is studied. Based on the correlative work about the agent synchronization, a modified model is presented, in which each com...The synchronization of time-delayed multi-agent networks with connected and directed topology is studied. Based on the correlative work about the agent synchronization, a modified model is presented, in which each communication receiver is distributed a delay 7. In addition, a proportional term k is introduced to modulate the delay range and to guarantee the synchronization of each agent. Two new parameters mentioned above are only correlative to the network topology, and a theorem about their connections is derived by both frequency domain method and geometric method. Finally, the theoretical result is illustrated by numerical simulations.展开更多
In this paper, an optimal H∞ control algorithm was applied to the design of an active tendon system installed at the first story of a multi-story building to reduce its interstory drift due to earthquake excitations....In this paper, an optimal H∞ control algorithm was applied to the design of an active tendon system installed at the first story of a multi-story building to reduce its interstory drift due to earthquake excitations. To achieve optimal control performance and to guarantee the stability of the control system, an optimum strategy to select control parameters γ and α was developed. Analytical expressions of the upper and the lower bounds of γ and α were obtained for a single degree-of-freedom system with state feedback control. The selection ranges for both γ and α are graphically defined so that the controlled system is always stable and the control performance is better than by the conventional LQR control algorithm. Numerical results from a controlled three-story building under real earthquake excitations demonstrate that the peak first interstory drift can be significantly reduced with maximum control force around 10% of the building weight. An optimum design flow chart was provided. In addition, for a time-delayed structure, this study gave explicit formulae to calculate the critical values of γ and a. The system stability and control performance can thus be guaranteed even with time delay.展开更多
Considering the impact of time delay in the lateral stiffness of the primary suspension and stochastic disturbances of equivalent conicity on the wheelset system, a stochastic time-delayed wheelset system is establish...Considering the impact of time delay in the lateral stiffness of the primary suspension and stochastic disturbances of equivalent conicity on the wheelset system, a stochastic time-delayed wheelset system is established. The wheelset system is transformed into a onedimensional Ito stochastic differential equation using central manifold and stochastic averaging methods. The analysis of the system's stochastic stability is conducted through the maximum Lyapunov exponent and singular boundary theory. The combination of the stationary probability density method and numerical simulation is employed to discuss the types and conditions of stochastic P-bifurcation in the wheelset system. The results indicate that changes in speed and time delay induce stochastic P-bifurcations in the wheelset system, while changes in noise intensity do not lead to stochastic P-bifurcations. Both time delay and equivalent conicity affect the critical speed of the wheelset system, and the critical speed gradually increases with the decrease of time delay and equivalent conicity.展开更多
Synchronization rhythm and oscillating in biological systems can give clues to understanding the cooperation and competition between cells under appropriate biological and physical conditions. As a result, the network...Synchronization rhythm and oscillating in biological systems can give clues to understanding the cooperation and competition between cells under appropriate biological and physical conditions. As a result, the network setting is appreciated to detect the stability and transition of collective behaviors in a network with different connection types. In this paper, the synchronization performance in time-delayed excitable homogeneous random networks（EHRNs） induced by diversity in system parameters is investigated by calculating the synchronization parameter and plotting the spatiotemporal evolution pattern, and distinct impacts induced by parameter-diversity are detected by setting different time delays. It is found that diversity has no distinct effect on the synchronization performance in EHRNs with small time delay being considered. When time delay is increased greatly, the synchronization performance of EHRN degenerates remarkably as diversity is increased. Surprisingly, by setting a moderate time delay, appropriate parameter-diversity can promote the synchronization performance in EHRNs, and can induce the synchronization transition from the asynchronous state to the weak synchronization. Moreover, the bistability phenomenon, which contains the states of asynchronous state and weak synchronization,is observed. Particularly, it is confirmed that the parameter-diversity promoted synchronization performance in time-delayed EHRN is manifested in the enhancement of the synchronization performance of individual oscillation and the increase of the number of synchronization transitions from the asynchronous state to the weak synchronization. Finally, we have revealed that this kind of parameter-diversity promoted synchronization performance is a robust phenomenon.展开更多
A high-order full-discretization method （FDM） using Hermite interpolation （HFDM） is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to ...A high-order full-discretization method （FDM） using Hermite interpolation （HFDM） is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.展开更多
Due to the appearance and the study of the ornithopter and flexible-wing micro air vehicles,etc.,the time-varying systems become more and more important and ubiquitous in the study of the mechanics.In this letter,the ...Due to the appearance and the study of the ornithopter and flexible-wing micro air vehicles,etc.,the time-varying systems become more and more important and ubiquitous in the study of the mechanics.In this letter,the sufficient conditions of the uniform asymptotic stability are first presented for the delayed time-varying linear differential equations with any time delay by employing the Dini derivative,Lozinskii measure and the generalized scalar Halanay delayed differential inequality.They are especially based on the estimation of the arbitrary solutions but not the fundamental solution matrix since their solutions'space is infinite-dimensional.Then some sufficient conditions of the stability,asymptotic stability and uniform asymptotic stability of the delayed time-varying linear system with a sufficiently small time delay are reported by employing Taylor expansion and Dini derivative.It implies that these stabilities can be guaranteed by the Lozinskii measure of the matrix composing of the time delay and the coefficient matrices of the system.展开更多
基金Project supported by the Science Foundation of Huazhong University of Science and Technology (Grant No 2006Q003B)
文摘This paper investigates the dynamical behaviour of the Liu system with time delayed feedback. Two typical situations are considered and the effect of time-delay parameter on the dynamics of the system is discussed. It is shown that the Liu system with time delayed feedback may exhibit interesting and extremely rich dynamical behaviour. The evolution of the dynamics is shown to be complex with varying time-delay parameter. Moreover, the strange attractor like ‘wormhole＇ is detected via numerical simulations.
基金Supported by the National Natural Science Foundation of China under Grant No.61681240393the Fundamental Research Funds for the Central Universities under Grant No.2015XKMS076
文摘This paper investigates the synchronization of time delayed complex dynamical networks with periodical on-off coupling. Both the theoretical and numerical results show that, in spite of time delays and on-off coupling, two networks may synchronize if the coupling strength and the on-off rate are large enough. It is shown that, for undirected and strongly connected networks, the upper bound of time delays for synchronization is a decreasing function of the absolute value of the minimum eigenvalue of the adjacency matrix. The theoretical analysis confirms the numerical results and provides a better understanding of the influence of time delays and on-off coupling on the synchronization transition. The influence of random delays on the synchronization is also discussed.
基金Supported by Funding for the National Natural Science Foundation of China(12201557,12001483,61807006)。
文摘Biologically,because of the impact of reproduction period and nonlocal dispersal of HIV-infected cells,time delay and spatial heterogeneity should be considered.In this paper,we establish an HIV infection model with nonlocal dispersal and infection age.Moreover,applying the theory of Fourier transformation and von Foerster rule,we transform the model to an integrodifferential equation with nonlocal time delay and dispersal.The well-posedness,positivity,and boundedness of the solution for the model are studied.
基金Supported by Research Project of Hubei Provincial Department of Education under Grant No. Q20101609Foundation of Wuhan Textile University under Grant No. 105040
文摘In this paper, we propose a method for the projective synchronization between two different chaotic systems with variable time delays. Using active control approach, the suitable controller is constructed to make the states of two different diverse time delayed systems asymptotically synchronize up to the desired scaling factor. Based on the Lyapunov stability theory, the sufficient condition for the projective synchronization is calculated theoretically. Numerical simulations of the projective synchronization between Maekey-Glass system and Ikeda system with variable time delays are shown to validate the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(Grant Nos.42407267 and 52374152)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20220975).
文摘Time-delayed blasting is widely utilized in engineering to mitigate induced vibration hazards and enhance fragmentation.The underlying vibration reduction principle is the decrease of the charge weight per delay,while the potential for further vibration reduction remains debated,largely due to unclear underlying mechanisms.In light of the popularization of electronic detonators and the representativeness of double-hole configurationsfor multiple blastholes,it is essential to investigate the vibration characteristics induced by time-delayed double blastholes.Therefore,a series of doubleborehole experimental blasts was conducted in an underground roadway to clarify the variation in vibration from single-hole to dual-hole conditions.Based on the experimental data and inherent limitations,an exact full-fieldtheoretical model was further employed to systematically analyze the effects of delay time,charge length,and borehole inclination angle on vibrations induced by various doublehole configurations.The experimental data and theoretical analysis reveal that the general scaled distance effectively predicts vibrations in delayed blasting but does not reflectvibration reduction.Increasing delay time causes fluctuatingPPVs,which stabilize slightly above single-hole PPVs as delay times exceed a certain value.The delayed blasting primarily reduces near-fieldfrequencies.Longer charge lengths in double boreholes increase PPV levels and attenuation rates within a certain length,and the vibration behavior of combined long and short charge lengths is governed by the long blasthole.Larger blasthole inclination angles enhance vibration amplitude and reduce PPV attenuation rates.Optimizing inclination angles is more critical than adjusting delay times,and parallel boreholes offer the best vibration control.
基金supported in part by the National Natural Science Foundation of China(No.51677107,52077126)。
文摘To investigate impact of time delays on the small signal stability of power systems, the least-damped eigenvalues with the smallest damping ratios have been calculated by eigen-analysis methods based on Solution Operator Discretization (SOD) with Pseudo-Spectral collocation (PS) and Implicit Runge-Kutta (IRK) methods. This paper evolves SOD-PSIIRK into their partial counterparts, i.e., PSOD-PSIIRK, with greatly enhanced efficiency and reliability in analyzing large-scale time delayed power systems. Compared with SOD-PSIIRK, PSOD-PSIIRK are characterized in constructing low order discretization matrices of solution operator as well as efficiently and directly solving the embedded Matrix-Inverse-Vector Products (MIVPs). The dimensions of the discretization matrices of solution operator are largely reduced as only the retarded state variables are discretized, rather than all state variables as in SOD-PSIIRK. Meanwhile, the proposed PSOD-PSIIRK optimize the most computationally expensive operations in SOD-PSIIRK by avoiding the iterative solutions to the two embedded MIVPs. PSOD-PS/IRK directly and efficiently compute the MIVPs via factorizing the Kronecker product-like discretization matrices of the solution operator into Schur complements. The Central China-North China ultra-high-voltage power grid with 80577 state variables serves to validate the proposed PSOD-PSIIRK and shows that compared with SOD-PSIIRK, the computational time consumed by PSOD-PSIIRK is cut down by 49.96 times without loss of any accuracy.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 61072029 and 11175067the Guangdong Provincial Natural Science Foundation under Grant Nos. 10151063101000025 and S2011010003323
文摘We study the transport of overdamped Brownian particles in a symmetricaJly periodic potential in the presence of an asymmetrically ac driving force and a time-delayed feedback. It is found that for low frequencies, the average velocity can be negative by changing the driving amplitude, for high frequencies, there exists an optimized driving amplitude at which the average velocity takes its maximum value. Additionally, there is a threshold value of driving amplitude below which no directed transport can be obtained for high frequencies. For the large value of the delay time, the average velocity is independent of the delay time.
基金supported by the National Natural Science Foundation of China(Grant Nos.51475246 and 51075215)the Natural Science Foundation of Jiangsu Province of China(Grant No.Bk20131402)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry of China(Grand No.[2012]1707)
文摘With the increase of system scale, time delays have become unavoidable in nonlinear power systems, which add the complexity of system dynamics and induce chaotic oscillation and even voltage collapse events. In this paper, coexisting phenomenon in a fourth-order time-delayed power system is investigated for the first time with different initial conditions.With the mechanical power, generator damping factor, exciter gain, and time delay varying, the specific characteristic of the time-delayed system, including a discontinuous ＂jump＂ bifurcation behavior is analyzed by bifurcation diagrams, phase portraits, Poincar′e maps, and power spectrums. Moreover, the coexistence of two different periodic orbits and chaotic attractors with periodic orbits are observed in the power system, respectively. The production condition and existent domain of the coexistence phenomenon are helpful to avoid undesirable behavior in time-delayed power systems.
基金supported by the National Natural Science Foundation of China (Grant No 70571017)the Research Foundation from Provincial Education Department of Zhejiang of China (Grant No 21186000507)
文摘Based on the fluid flow time-delayed model proposed by Misra et al in internet congestion control, one modified time-delayed model is presented, where the influence of the communication delay on the router queue length is investigated in detail. The main advantage of the new model is that its stability domain is larger even without an extra controller. By linear stability analysis and numerical simulation, tbe effectiveness and feasibility of the novel model in internet congestion control are verified.
基金supported by National Natural Science Foundationof China(Nos.11261010 and 11101126)Soft Science and TechnologyProgram of Guizhou Province(No.2011LKC2030)+2 种基金Natural Scienceand Technology Foundation of Guizhou Province(No.J[2012]2100)Governor Foundation of Guizhou Province(No.[2012]53)Doctoral Foundation of Guizhou University of Finance and Economics
文摘In this paper, the control of chemical chaotic dynamical system is investigated by time-delayed feedback control technique.The controllability and the stability of the equilibriums and local Hopf bifurcation of the system are verified. Some numerical simulations which show the effectiveness of the time-delayed feedback control method are provided.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10975043 and 10947166)the Natural Science Foundation of Hebei Province,China (Grant Nos. A2011201006 and A2010000185)the Science Foundation of Hebei University
文摘The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of the time delay on the Turing and Hopf instabilities near the Turing Hopf codimension-two phase space. Numerical simulations show that the transition between the Turing patterns （hexagon, stripe, and honeycomb）, the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and Hopf instabilities. Our results have shown the flexibility of the time delay on controlling the pattern formations near the Turing-Hopf codimension-two phase space.
基金Supported by the Anhui Provincial Department of National Land and Resources with their Science and Technology Project entitled "Research on a Dynamic Monitoring Land Usage,Evaluation and Decision Support Management System in Wanjiang Demonstration Area"(Grant No.2011-K-23)Anhui Agricultural University,China(Grant No.YJ2012-03,No.XK2013029 and No.11201002)The Natural Sciences and Engineering Research Council of Canada
文摘A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model, we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed prey to predator in the Ivlev-type functional responses. The existence and uniqueness of the positive equilibrium of the model and the stability of the equilibrium of the model are studied under various conditions. Hopf bifurcation analysis of the delayed model is provided.
基金Project supported in part by the National Natural Science Foundation of China (Grant No. 61973064)the Natural Science Foundation of Hebei Province of China (Grant Nos. F2019501126 and F2022501024)+1 种基金the Natural Science Foundation of Liaoning Province, China (Grant No. 2020-KF11-03)the Fund from Hong Kong Research Grants Council (Grant No. CityU11206320)。
文摘Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the effects of noise, time delay,and their inner interactions on the network synchronization. It is found that when there exists time-delayed coupling in the network and noise diffuses through all state variables of nodes, appropriately increasing the noise intensity can effectively improve the network synchronizability;otherwise, noise can be either beneficial or harmful. For stochastic networks, large time delays will lead to desynchronization. These findings provide valuable references for designing optimal complex networks in practical applications.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61203047 and 60904023)
文摘We consider the robust stabilization problem for discrete-time Takagi-Sugeno （T S） fuzzy systems with time- varied delays subjected to input saturation. We design static and dynamic anti-windup fuzzy controllers to ensure the convergence of all admissible initial states within the domain of attraction. Based on the project lemma and classical sector conditions, the conditions for the existence of solutions to this problem are obtained and expressed in terms of a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design approach.
基金the National Natural Science Foundation of China (No. 70571017)the Research Foundation from Provincial Education Department of Zhejiang of China (No. 20070928)
文摘The synchronization of time-delayed multi-agent networks with connected and directed topology is studied. Based on the correlative work about the agent synchronization, a modified model is presented, in which each communication receiver is distributed a delay 7. In addition, a proportional term k is introduced to modulate the delay range and to guarantee the synchronization of each agent. Two new parameters mentioned above are only correlative to the network topology, and a theorem about their connections is derived by both frequency domain method and geometric method. Finally, the theoretical result is illustrated by numerical simulations.
基金Ministry of Education and the Science Council (NSC) of Taiwan Under the ATU plan and Grants No. NSC 95-2625-Z-005-009
文摘In this paper, an optimal H∞ control algorithm was applied to the design of an active tendon system installed at the first story of a multi-story building to reduce its interstory drift due to earthquake excitations. To achieve optimal control performance and to guarantee the stability of the control system, an optimum strategy to select control parameters γ and α was developed. Analytical expressions of the upper and the lower bounds of γ and α were obtained for a single degree-of-freedom system with state feedback control. The selection ranges for both γ and α are graphically defined so that the controlled system is always stable and the control performance is better than by the conventional LQR control algorithm. Numerical results from a controlled three-story building under real earthquake excitations demonstrate that the peak first interstory drift can be significantly reduced with maximum control force around 10% of the building weight. An optimum design flow chart was provided. In addition, for a time-delayed structure, this study gave explicit formulae to calculate the critical values of γ and a. The system stability and control performance can thus be guaranteed even with time delay.
基金Supported by the National Natural Science Foundation of China (61863022)the Key Project of Gansu Province Natural Science Foundation(23JRRA882)。
文摘Considering the impact of time delay in the lateral stiffness of the primary suspension and stochastic disturbances of equivalent conicity on the wheelset system, a stochastic time-delayed wheelset system is established. The wheelset system is transformed into a onedimensional Ito stochastic differential equation using central manifold and stochastic averaging methods. The analysis of the system's stochastic stability is conducted through the maximum Lyapunov exponent and singular boundary theory. The combination of the stationary probability density method and numerical simulation is employed to discuss the types and conditions of stochastic P-bifurcation in the wheelset system. The results indicate that changes in speed and time delay induce stochastic P-bifurcations in the wheelset system, while changes in noise intensity do not lead to stochastic P-bifurcations. Both time delay and equivalent conicity affect the critical speed of the wheelset system, and the critical speed gradually increases with the decrease of time delay and equivalent conicity.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11675001,11675112,11775020,and 11372122)
文摘Synchronization rhythm and oscillating in biological systems can give clues to understanding the cooperation and competition between cells under appropriate biological and physical conditions. As a result, the network setting is appreciated to detect the stability and transition of collective behaviors in a network with different connection types. In this paper, the synchronization performance in time-delayed excitable homogeneous random networks（EHRNs） induced by diversity in system parameters is investigated by calculating the synchronization parameter and plotting the spatiotemporal evolution pattern, and distinct impacts induced by parameter-diversity are detected by setting different time delays. It is found that diversity has no distinct effect on the synchronization performance in EHRNs with small time delay being considered. When time delay is increased greatly, the synchronization performance of EHRN degenerates remarkably as diversity is increased. Surprisingly, by setting a moderate time delay, appropriate parameter-diversity can promote the synchronization performance in EHRNs, and can induce the synchronization transition from the asynchronous state to the weak synchronization. Moreover, the bistability phenomenon, which contains the states of asynchronous state and weak synchronization,is observed. Particularly, it is confirmed that the parameter-diversity promoted synchronization performance in time-delayed EHRN is manifested in the enhancement of the synchronization performance of individual oscillation and the increase of the number of synchronization transitions from the asynchronous state to the weak synchronization. Finally, we have revealed that this kind of parameter-diversity promoted synchronization performance is a robust phenomenon.
基金partially supported by a scholarship from the China Scholarship Councilthe German Research Foundation (DFG) for financial support within the Cluster of Excellence in Simulation Technology (EXC 310) at the University of Stuttgart
文摘A high-order full-discretization method （FDM） using Hermite interpolation （HFDM） is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.
基金supported by the National Natural Science Foundation of China(10702065 and 11372282)
文摘Due to the appearance and the study of the ornithopter and flexible-wing micro air vehicles,etc.,the time-varying systems become more and more important and ubiquitous in the study of the mechanics.In this letter,the sufficient conditions of the uniform asymptotic stability are first presented for the delayed time-varying linear differential equations with any time delay by employing the Dini derivative,Lozinskii measure and the generalized scalar Halanay delayed differential inequality.They are especially based on the estimation of the arbitrary solutions but not the fundamental solution matrix since their solutions'space is infinite-dimensional.Then some sufficient conditions of the stability,asymptotic stability and uniform asymptotic stability of the delayed time-varying linear system with a sufficiently small time delay are reported by employing Taylor expansion and Dini derivative.It implies that these stabilities can be guaranteed by the Lozinskii measure of the matrix composing of the time delay and the coefficient matrices of the system.
