Modified projective and modified function projective synchronization of a class of real nonlinear systems and a class of complex nonlinear systems

The modified projective and modified function projective synchronization of a class of chaotic real nonlinear systems, or a class of chaotic complex nonlinear systems, have been widely reported in the previous studies, respectively. In the paper, the modified projective and modified function projective synchronization between a class of chaotic real nonlinear systems and a class of chaotic complex nonlinear systems are first investigated. Based on the Lyapunov stability theory, the drive real system and response complex system can be synchronized up to the desired scaling constants and functions, respectively. The corresponding numerical simulations are performed to verify and demonstrate the validity and feasibility of the presented idea.

[1]  Hsien-Keng Chen,et al.  Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen–Lee systems , 2010 .

[2]  Emad E. Mahmoud,et al.  Complete synchronization of chaotic complex nonlinear systems with uncertain parameters , 2010 .

[3]  A. Hramov,et al.  Time scale synchronization of chaotic oscillators , 2005, nlin/0602053.

[4]  Yi Shen,et al.  General hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameter identification in several chaotic and hyperchaotic systems , 2013 .

[5]  Junwei Sun,et al.  Transmission projective synchronization of multi-systems with non-delayed and delayed coupling via impulsive control. , 2012, Chaos.

[6]  Luo Runzi,et al.  Combination synchronization of three classic chaotic systems using active backstepping design. , 2011, Chaos.

[7]  Guangzhao Cui,et al.  Combination–combination synchronization among four identical or different chaotic systems , 2013 .

[8]  S. Bishop,et al.  Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems. , 2001, Chaos.

[9]  Yi Shen,et al.  Compound synchronization of four memristor chaotic oscillator systems and secure communication. , 2013, Chaos.

[10]  Dibakar Ghosh,et al.  Nonlinear active observer-based generalized synchronization in time-delayed systems , 2009 .

[11]  Guanrong Chen,et al.  Chaos synchronization in fractional differential systems , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  Ming-Chung Ho,et al.  Phase and anti-phase synchronization of two chaotic systems by using active control , 2002 .

[13]  P. K. Roy,et al.  Lag synchronization and scaling of chaotic attractor in coupled system. , 2012, Chaos.

[14]  Gangquan Si,et al.  Adaptive generalized function matrix projective lag synchronization of uncertain complex dynamical networks with different dimensions , 2013 .

[15]  Quan Yin,et al.  Compound synchronization for four chaotic systems of integer order and fractional order , 2014 .

[16]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[17]  Chao Luo,et al.  Hybrid modified function projective synchronization of two different dimensional complex nonlinear systems with parameters identification , 2013, J. Frankl. Inst..

[18]  Jie Chen,et al.  Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control , 2014 .

[19]  Xin-Ming Cheng,et al.  A Novel Scheme Adaptive Hybrid Dislocated Synchronization for Two Identical and Different Memristor Chaotic Oscillator Systems with Uncertain Parameters , 2014 .

[20]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[21]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[22]  Ling Lü,et al.  Generalized synchronization of spatiotemporal chaos in a weighted complex network , 2011 .

[23]  Zuolei Wang.  Projective synchronization of hyperchaotic Lü system and Liu system , 2010 .

[24]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[25]  Tassos Bountis,et al.  Active Control and Global Synchronization of the Complex Chen and lÜ Systems , 2007, Int. J. Bifurc. Chaos.

[26]  Emad E. Mahmoud,et al.  On the hyperchaotic complex Lü system , 2009 .

[27]  Daolin Xu,et al.  Stability criterion for projective synchronization in three-dimensional chaotic systems , 2001 .

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

[29]  Emad E. Mahmoud,et al.  Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems , 2010 .

[30]  Daolin Xu,et al.  Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems , 2005 .

[31]  Gamal M. Mahmoud,et al.  Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system , 2007 .

[32]  Yong Chen,et al.  Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives , 2008, Appl. Math. Comput..

[33]  Mark J. McGuinness,et al.  The complex Lorenz equations , 1982 .

[34]  Xiangjun Wu,et al.  Adaptive generalized function projective synchronization of uncertain chaotic complex systems , 2013, Nonlinear Dynamics.

[35]  Jianping Yan,et al.  Generalized projective synchronization of a unified chaotic system , 2005 .

[36]  Yen-Sheng Chen,et al.  Synchronization of unidirectional coupled chaotic systems via partial stability , 2004 .

[37]  Guohui Li.  Modified projective synchronization of chaotic system , 2007 .

[38]  Her-Terng Yau,et al.  Synchronization and anti-synchronization coexist in two-degree-of-freedom dissipative gyroscope with nonlinear inputs , 2008 .

[39]  Daolin Xu,et al.  Criteria for the occurrence of projective synchronization in chaotic systems of arbitrary dimension , 2002 .