Tracking the state of the delay hyperchaotic Lü system using the coullet chaotic system via a single controller

In this article, a partial synchronization scheme is proposed based on Lyapunov stability theory to track the signal of the delay hyperchaotic Lu system using the Coullet system based on only one single controller. The proposed tracking control design has two advantages: only one controller is adopted in our approach and it can allow us to drive the hyperchaotic system to a simple chaotic system even with uncertain parameters. Numerical simulation results are given to demonstrate the effectiveness and robustness of the proposed partial synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity, 2014

[1]  Xue-Rong Shi,et al.  Chaotic bursting lag synchronization of Hindmarsh-Rose system via a single controller , 2009, Appl. Math. Comput..

[2]  Yongjian Liu,et al.  A new hyperchaotic system from the Lü system and its control , 2011, J. Comput. Appl. Math..

[3]  Jun Ma,et al.  Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system , 2011 .

[4]  Thang Manh Hoang,et al.  A New Secure Communication Model Based on Synchronization of Coupled Multidelay Feedback Systems , 2010 .

[5]  Ping He,et al.  Robust adaptive synchronization of uncertain complex networks with multiple time-varying coupled delays , 2015, Complex..

[6]  Xuerong Shi,et al.  The alternating between complete synchronization and hybrid synchronization of hyperchaotic Lorenz system with time delay , 2012 .

[7]  Jun Tang,et al.  Simulating the electric activity of FitzHugh–Nagumo neuron by using Josephson junction model , 2012 .

[8]  Keming Tang,et al.  Synchronization of delay bursting neuron system with stochastic noise via linear controllers , 2014, Appl. Math. Comput..

[9]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[10]  Yun Chen,et al.  Global anti-synchronization of master-slave chaotic modified Chua's circuits coupled by linear feedback control , 2010, Math. Comput. Model..

[11]  Hongjun Gao,et al.  Adjustment of spiral drift by a travelling wave perturbation , 2012 .

[12]  Dibakar Ghosh Nonlinear-observer–based synchronization scheme for multiparameter estimation , 2008 .

[13]  Teh-Lu Liao,et al.  Adaptive synchronization of chaotic systems and its application to secure communications , 2000 .

[14]  Xingyuan Wang,et al.  A simple criterion for impulsive chaotic synchronization , 2011 .

[15]  Zhengzhi Han,et al.  Controlling and synchronizing chaotic Genesio system via nonlinear feedback control , 2003 .

[16]  Yao-Lin Jiang,et al.  Synchronization of multiple bursting neurons ring coupled via impulsive variables , 2015, Complex..

[17]  J. B. Chabi Orou,et al.  Synchronization dynamics in a ring of four mutually coupled biological systems , 2008 .

[18]  Tao Fan,et al.  Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties , 2014, Complex..

[19]  Ma Jun,et al.  Simulated test of electric activity of neurons by using Josephson junction based on synchronization scheme , 2012 .

[20]  P. Rana,et al.  Economic integration and synchronization of business cycles in East Asia , 2007 .

[21]  José Manoel Balthazar,et al.  On control and synchronization in chaotic and hyperchaotic systems via linear feedback control , 2008 .

[22]  Hongli Li,et al.  Impulsive synchronization of time delay bursting neuron systems with unidirectional coupling , 2015, Complex..

[23]  Alain Arneodo,et al.  Transition to stochasticity for a class of forced oscillators , 1979 .

[24]  Xiaofeng Liao,et al.  Impulsive synchronization of nonlinear coupled chaotic systems , 2004 .

[25]  Saleh Mobayen,et al.  Design of a robust tracker and disturbance attenuator for uncertain systems with time delays , 2015, Complex..

[26]  Z. Ge,et al.  Phase synchronization of coupled chaotic multiple time scales systems , 2004 .

[27]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[28]  Chun-Lai Li,et al.  Tracking control and generalized projective synchronization of a class of hyperchaotic system with unknown parameter and disturbance , 2012 .

[29]  Vladimir E. Bondarenko,et al.  Information processing, memories, and synchronization in chaotic neural network with the time delay , 2005, Complex..

[30]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[31]  Ayub Khan,et al.  Synchronization of circular restricted three body problem with lorenz hyper chaotic system using a robust adaptive sliding mode controller , 2013, Complex..

[32]  Yao-Chen Hung,et al.  Synchronization of two different systems by using generalized active control , 2002 .

[33]  Keming Tang,et al.  Pinning synchronization of unilateral coupling neuron network with stochastic noise , 2014, Appl. Math. Comput..

[34]  J. Cao,et al.  Periodic oscillatory solution of bidirectional associative memory networks with delays. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.