Generalized Combination Complex Synchronization for Fractional-Order Chaotic Complex Systems

Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we design a general controller via active control. Additionally, by virtue of two complex scaling matrices, generalized combination complex synchronization between fractional-order chaotic complex systems and real systems is investigated. Finally, three typical examples are given to demonstrate the effectiveness and feasibility of the schemes.

[1]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[2]  Chunguang Li,et al.  Chaos and hyperchaos in the fractional-order Rössler equations , 2004 .

[3]  Pagavathigounder Balasubramaniam,et al.  Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography , 2013, Nonlinear Dynamics.

[4]  Carl F. Lorenzo,et al.  Initialization of Fractional Differential Equations: Theory and Application , 2007 .

[5]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[6]  Xiangjun Wu,et al.  Generalized projective synchronization of the fractional-order Chen hyperchaotic system , 2009 .

[7]  Hadi Taghvafard,et al.  Phase and anti-phase synchronization of fractional order chaotic systems via active control , 2011 .

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

[9]  Chao Luo,et al.  A New Fractional-Order Chaotic Complex System and Its Antisynchronization , 2014 .

[10]  Xiaobing Zhou,et al.  Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems , 2014 .

[11]  Pagavathigounder Balasubramaniam,et al.  Synchronization of a novel fractional order stretch-twist-fold (STF) flow chaotic system and its application to a new authenticated encryption scheme (AES) , 2014, Nonlinear Dynamics.

[12]  Jian Liu,et al.  Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos , 2014, Entropy.

[13]  Ping Zhou,et al.  A new 4-D non-equilibrium fractional-order chaotic system and its circuit implementation , 2014, Commun. Nonlinear Sci. Numer. Simul..

[14]  Ling Hong,et al.  Fractional-order complex T system: bifurcations, chaos control, and synchronization , 2014 .

[15]  Wenquan Chen,et al.  Projective synchronization of different fractional-order chaotic systems with non-identical orders , 2012 .

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

[17]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[18]  Nathalie Corson,et al.  Synchronization of Chaotic fractional-Order Systems via Linear Control , 2010, Int. J. Bifurc. Chaos.

[19]  Guangzhao Cui,et al.  Combination complex synchronization of three chaotic complex systems , 2015 .

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

[21]  Zaihua Wang,et al.  Correcting the initialization of models with fractional derivatives via history-dependent conditions , 2016 .

[22]  Xingyuan Wang,et al.  Chaos in the fractional-order complex Lorenz system and its synchronization , 2013 .

[23]  Andrew Y. T. Leung,et al.  Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method , 2014 .

[24]  P. Balasubramaniam,et al.  Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system , 2015 .

[25]  D. Matignon.  Stability results for fractional differential equations with applications to control processing , 1996 .

[26]  P. Balasubramaniam,et al.  Fast projective synchronization of fractional order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (DOB) , 2015 .

[27]  M. Haeri,et al.  Synchronization of chaotic fractional-order systems via active sliding mode controller , 2008 .

[28]  Xingyuan Wang,et al.  CHAOS GENERATED FROM THE FRACTIONAL-ORDER COMPLEX CHEN SYSTEM AND ITS APPLICATION TO DIGITAL SECURE COMMUNICATION , 2013 .

[29]  Enrico Scalas,et al.  Applications of Continuous-Time Random Walks to Finance and Economics , 2012 .

[30]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[31]  Enrico Scalas,et al.  The application of continuous-time random walks in finance and economics , 2006 .

[32]  Xinchu Fu,et al.  Combination synchronization of three different order nonlinear systems using active backstepping design , 2013 .

[33]  Subir Das,et al.  Synchronization of fractional order chaotic systems using active control method , 2012 .

[34]  T. Hartley,et al.  Dynamics and Control of Initialized Fractional-Order Systems , 2002 .

[35]  P. Balasubramaniam,et al.  Synchronization and an application of a novel fractional order King Cobra chaotic system. , 2014, Chaos.

[36]  Xiaobing Zhou,et al.  Combination Synchronization of Three Identical or Different Nonlinear Complex Hyperchaotic Systems , 2013, Entropy.