Synchronisation control of composite chaotic systems

ABSTRACT Synchronisation conditions are studied for composite chaotic systems with complex compound structure and the signum function based on the theorem of zero-solution stability for a class of linear time-varying systems with countable discontinuous points. The synchronisation controller and its gain range are deduced according to the stability theorem, where the gain of the controller can speed synchronisation. Numerical simulation further proves the control theory and the validity of the synchronisation controller. The proposed controller can be widely applied in those chaotic systems with switch functions or other hybrid chaotic systems.

[1]  Mohamed Darouach,et al.  Group synchronization and control of a new class of adaptive complex network with Brownian Motion and Time-varying Delay , 2014, 2014 European Control Conference (ECC).

[2]  V. K. Chandrasekar,et al.  Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Julien Clinton Sprott,et al.  Elementary quadratic chaotic flows with a single non-hyperbolic equilibrium , 2015 .

[4]  Julien Clinton Sprott,et al.  Simple chaotic flows with a line equilibrium , 2013 .

[5]  Guan Xin-ping,et al.  THE ADAPTIVE CONTROL OF CHEN’S CHAOTIC SYSTEM , 2001 .

[6]  Hongtao Lu,et al.  Synchronization of a new fractional-order hyperchaotic system , 2009 .

[7]  Xing-yuan Wang,et al.  Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control , 2009 .

[8]  Xing-yuan Wang,et al.  Dynamic analysis of the fractional-order Liu system and its synchronization. , 2007, Chaos.

[9]  Yuhua Xu,et al.  Adaptive synchronization of stochastic time-varying delay dynamical networks with complex-variable systems , 2015 .

[10]  Xinghuo Yu,et al.  Design and Implementation of Grid Multiwing Hyperchaotic Lorenz System Family via Switching Control and Constructing Super-Heteroclinic Loops , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Zhouchao Wei,et al.  Hidden Attractors and Dynamical Behaviors in an Extended Rikitake System , 2015, Int. J. Bifurc. Chaos.

[12]  Mingjun Wang,et al.  A chaotic secure communication scheme based on observer , 2009 .

[13]  Yuanyuan Huang,et al.  Delay-dependent synchronization for non-diffusively coupled time-varying complex dynamical networks , 2015, Appl. Math. Comput..

[14]  Julien Clinton Sprott,et al.  Coexistence of Point, periodic and Strange attractors , 2013, Int. J. Bifurc. Chaos.

[15]  Jürgen Kurths,et al.  Generalizing the transition from amplitude to oscillation death in coupled oscillators. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Punit Parmananda,et al.  Synchronization using linear and nonlinear feedbacks: a comparison , 1998 .

[17]  Zhang Liping,et al.  Non-smooth bifurcation analysis of Chen system via impulsive force , 2012 .

[18]  Da Lin,et al.  Self-organizing adaptive fuzzy neural control for the synchronization of uncertain chaotic systems with random-varying parameters , 2011, Neurocomputing.

[19]  Xinghuo Yu,et al.  Generating Grid Multiwing Chaotic Attractors by Constructing Heteroclinic Loops Into Switching Systems , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[20]  Mohamed Darouach,et al.  Exponential synchronization for a new class of complex dynamical network with PIPC and hybrid TVD , 2014, 2014 IEEE International Symposium on Intelligent Control (ISIC).

[21]  Li Chun-Biao,et al.  Study on the generalized projective synchronization of improved invariable-Lyapunov-exponent-spectrum chaotic system , 2009 .

[22]  Diyi Chen,et al.  Synchronization between integer-order chaotic systems and a class of fractional-order chaotic system based on fuzzy sliding mode control , 2012 .

[23]  Da Lin,et al.  Observer-based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation , 2010, Fuzzy Sets Syst..

[24]  Dequan Li,et al.  Synchronization of Three-Scroll Unified Chaotic System (TSUCS) and its hyper-chaotic system using active pinning control , 2013 .

[25]  M. Yao,et al.  Study of hidden attractors, multiple limit cycles from Hopf bifurcation and boundedness of motion in the generalized hyperchaotic Rabinovich system , 2015 .

[26]  Zhaoyan Wu.  Synchronization of discrete dynamical networks with non-delayed and delayed coupling , 2015, Appl. Math. Comput..

[27]  Da Lin,et al.  Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems , 2010, Neurocomputing.

[28]  Hao Shen,et al.  Mixed H∞/passive synchronization for complex dynamical networks with sampled-data control , 2015, Appl. Math. Comput..

[29]  Li Chun-Biao,et al.  Synchronization methods and properties of the improved chaotic system with constant Lyapunov exponent spectrum , 2010 .

[30]  Junwei Sun,et al.  Adaptive generalized hybrid function projective dislocated synchronization of new four-dimensional uncertain chaotic systems , 2015, Appl. Math. Comput..

[31]  Xing-yuan Wang,et al.  Projective synchronization of fractional order chaotic system based on linear separation , 2008 .

[32]  Guanrong Chen,et al.  Design and Implementation of Compound Chaotic attractors , 2012, Int. J. Bifurc. Chaos.

[33]  Guanrong Chen,et al.  On feedback-controlled synchronization of chaotic systems , 2003, Int. J. Syst. Sci..

[34]  Xinghuo Yu,et al.  Design and Implementation of Grid Multiwing Butterfly Chaotic Attractors From a Piecewise Lorenz System , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[35]  Ahmed S. Elwakil,et al.  A Four-Wing Butterfly Attractor from a Fully Autonomous System , 2003, Int. J. Bifurc. Chaos.

[36]  Diyi Chen,et al.  Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control. , 2012, Chaos.

[37]  Long Zhou,et al.  Chaos Multiscale-Synchronization between Two Different fractional-Order hyperchaotic Systems Based on Feedback Control , 2013, Int. J. Bifurc. Chaos.