Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding o...Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding of the dynamics of such circuits described by delay differential equations, Hopf bifurcation in the circuit is analysed using the Hopf bifurcation theory and the central manifold theorem in this paper. Bifurcation points and bifurcation directions are derived in detail, which prove to be consistent with the previous bifurcation diagram. Numerical simulations and experimental results are given to verify the theoretical analysis. Hopf bifurcation analysis can explain and predict the periodical orbit （oscillation） in Chen circuit with direct time delay feedback. Bifurcation boundaries are derived using the Hopf bifurcation analysis, which will be helpful for determining the parameters in the stabilisation of the originally chaotic circuit.展开更多
A delayed position feedback control is applied on DC of a typical MEMS resonator actuated by electrostatic forces voltage source for suppressing chaos A theoretical necessary condition for chaotic oscillation of the c...A delayed position feedback control is applied on DC of a typical MEMS resonator actuated by electrostatic forces voltage source for suppressing chaos A theoretical necessary condition for chaotic oscillation of the controlled system is presented. Numerical results and the analytical prediction reveal the evolution of dynamical behavior of the system with AC voltage amplitude and the control effect of delayed feedback on reducing chaos of the system. It shows that the delayed feedback control is effective on suppressing chaos of the micro mechanical resonator.展开更多
This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model （DFHM） with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto t...This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model （DFHM） with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto theorem, it is proven that the chaos generated by this controller satisfies the Li-Yorke definition. An example is presented to demonstrate the effectiveness of the approach.展开更多
A theoretical model has been developed to study nonlinear behaviors in a GaAs/AlGaAs heterostructure. We show that the system can exhibit chaotic oscillations under transverse magnetic fields and an electric field.The...A theoretical model has been developed to study nonlinear behaviors in a GaAs/AlGaAs heterostructure. We show that the system can exhibit chaotic oscillations under transverse magnetic fields and an electric field.The time-delayed feedback method was applied to stabilize the unstable periodic orbits（UPOs） embedded in the chaotic attractor.A bifurcation specified by a successive decrease in the number of UPOs with delayed time and feedback strength was revealed,indicating the stabilization of UPOs under feedback control.Noticeably,the introduction of a feedback perturbation will sometimes induce chaotic states that do not exist in the unperturbed system.展开更多
As a classical technique for chaos suppression,the time-delayed feedback controlling strategy has been widely developed by stabilizing unstable periodic orbits(UPOs)embedded in chaotic systems.A critical issue for ach...As a classical technique for chaos suppression,the time-delayed feedback controlling strategy has been widely developed by stabilizing unstable periodic orbits(UPOs)embedded in chaotic systems.A critical issue for achieving high controlling precision is to search for an appropriate time delay.This paper proposes a simple yet effective approach,based on incremental harmonic balance method,to determine the optimal time delay in the delayed feedback controller.The time delay is adjusted within the iterative scheme provided by the proposed method,and finally converges to the period of the target UPO.As long as the optimal time delay is fixed,moreover,the attained solution makes it quite convenient to analyze its stability according to the Floquet theory,which further provides the effective interval of the feedback gain.展开更多
This paper focuses on the issue of resilient dynamic output-feedback(DOF)control for H_∞synchronization of chaotic Hopfield networks with time-varying delay.The aim is to determine a DOF controller with gain perturba...This paper focuses on the issue of resilient dynamic output-feedback(DOF)control for H_∞synchronization of chaotic Hopfield networks with time-varying delay.The aim is to determine a DOF controller with gain perturbations ensuring that the H_∞norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound.A delaydependent criterion for the H_∞synchronization is derived by employing the Lyapunov functional method together with some recent inequalities.Then,with the help of some decoupling techniques,sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases.Lastly,an example is used to illustrate the applicability of the results obtained.展开更多
基金Project supported in part by the National Natural Science Foundation of China (Grant No. 60804040)Fok Ying-Tong Education Foundation for Young Teacher (Grant No. 111065)
文摘Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding of the dynamics of such circuits described by delay differential equations, Hopf bifurcation in the circuit is analysed using the Hopf bifurcation theory and the central manifold theorem in this paper. Bifurcation points and bifurcation directions are derived in detail, which prove to be consistent with the previous bifurcation diagram. Numerical simulations and experimental results are given to verify the theoretical analysis. Hopf bifurcation analysis can explain and predict the periodical orbit （oscillation） in Chen circuit with direct time delay feedback. Bifurcation boundaries are derived using the Hopf bifurcation analysis, which will be helpful for determining the parameters in the stabilisation of the originally chaotic circuit.
基金supported by the National Natural Science Foundation of China(10902071)"Chen Guang" Project of Shanghai Municipal Education Commission(11CG61)+1 种基金Leading Academic Discipline Project of Shanghai Institute of Technology(1020Q121001)Shanghai Leading Academic Discipline Project(J51501)
文摘A delayed position feedback control is applied on DC of a typical MEMS resonator actuated by electrostatic forces voltage source for suppressing chaos A theoretical necessary condition for chaotic oscillation of the controlled system is presented. Numerical results and the analytical prediction reveal the evolution of dynamical behavior of the system with AC voltage amplitude and the control effect of delayed feedback on reducing chaos of the system. It shows that the delayed feedback control is effective on suppressing chaos of the micro mechanical resonator.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60325311,60534010,60572070 and 60521003)the Program for Cheung Kong Scholars and Innovative Research Team in University (Grant No IRT0421)
文摘This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model （DFHM） with uncertain parameters. A simple nonlinear state feedback controller is designed for this purpose. By revised Marotto theorem, it is proven that the chaos generated by this controller satisfies the Li-Yorke definition. An example is presented to demonstrate the effectiveness of the approach.
文摘A theoretical model has been developed to study nonlinear behaviors in a GaAs/AlGaAs heterostructure. We show that the system can exhibit chaotic oscillations under transverse magnetic fields and an electric field.The time-delayed feedback method was applied to stabilize the unstable periodic orbits（UPOs） embedded in the chaotic attractor.A bifurcation specified by a successive decrease in the number of UPOs with delayed time and feedback strength was revealed,indicating the stabilization of UPOs under feedback control.Noticeably,the introduction of a feedback perturbation will sometimes induce chaotic states that do not exist in the unperturbed system.
基金supported by the National Natural Science Foundation of China(Grants 11702333 and 11672337)Natural Science Foundation of Guangdong Province(Grant 2018B030311001).
文摘As a classical technique for chaos suppression,the time-delayed feedback controlling strategy has been widely developed by stabilizing unstable periodic orbits(UPOs)embedded in chaotic systems.A critical issue for achieving high controlling precision is to search for an appropriate time delay.This paper proposes a simple yet effective approach,based on incremental harmonic balance method,to determine the optimal time delay in the delayed feedback controller.The time delay is adjusted within the iterative scheme provided by the proposed method,and finally converges to the period of the target UPO.As long as the optimal time delay is fixed,moreover,the attained solution makes it quite convenient to analyze its stability according to the Floquet theory,which further provides the effective interval of the feedback gain.
基金supported by the Natural Science Foundation of the Anhui Higher Education Institutions(Grant Nos.KJ2017A064 and KJ2018ZD007)the Excellent Youth Talent Support Program of Universities in Anhui Province(Grant No.GXYQZD2019021)the National Natural Science Foundation of China(Grant No.61503002).
文摘This paper focuses on the issue of resilient dynamic output-feedback(DOF)control for H_∞synchronization of chaotic Hopfield networks with time-varying delay.The aim is to determine a DOF controller with gain perturbations ensuring that the H_∞norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound.A delaydependent criterion for the H_∞synchronization is derived by employing the Lyapunov functional method together with some recent inequalities.Then,with the help of some decoupling techniques,sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases.Lastly,an example is used to illustrate the applicability of the results obtained.
