Triple Compound Synchronization Among Eight Chaotic Systems with External Disturbances via Nonlinear Approach

In this article, the authors have studied the triple compound synchronization among eight chaotic systems with external disturbances. The nonlinear approach is used to achieve triple compound synchronization among eight chaotic systems. The control functions are designed using Lyapunov stability theory. Numerical simulation and graphical results are carried out using the Runge–Kutta method, which shows that the designing of control functions are very effective and reliable and can be applied for triple compound synchronization among chaotic systems. The salient feature of the article is the exhibition of complexity in the error function in triple compound synchronization for which the communication via signals will be more secured through this type of synchronization process.

[1]  Jun-an Lu,et al.  Dual synchronization based on two different chaotic systems , 2007 .

[2]  Ayman A. Arafa,et al.  Projective synchronization for coupled partially linear complex‐variable systems with known parameters , 2017 .

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

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

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

[6]  Elena Grigorenko,et al.  Chaotic dynamics of the fractional Lorenz system. , 2003, Physical review letters.

[7]  Vijay K. Yadav,et al.  Comparative study of synchronization methods of fractional order chaotic systems , 2016 .

[8]  Sonia Hammami.  Multi-switching combination synchronization of discrete-time hyperchaotic systems for encrypted audio communication , 2019, IMA J. Math. Control. Inf..

[9]  Guanrong Chen,et al.  Analysis of a new chaotic system , 2005 .

[10]  Bernd Blasius,et al.  Complex dynamics and phase synchronization in spatially extended ecological systems , 1999, Nature.

[11]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[12]  Mohammad Saleh Tavazoei,et al.  Synchronization of uncertain chaotic systems using active sliding mode control , 2007 .

[13]  Hongyue Du,et al.  Modified function projective synchronization of chaotic system , 2009 .

[14]  Vijay K. Yadav,et al.  Phase and anti-phase synchronizations of fractional order hyperchaotic systems with uncertainties and external disturbances using nonlinear active control method , 2017 .

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

[16]  Edgar Knobloch,et al.  Chaos in the segmented disc dynamo , 1981 .

[17]  Yi Shen,et al.  Compound-combination synchronization of five chaotic systems via nonlinear control , 2016 .

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

[19]  M. T. Yassen,et al.  Chaos control of Chen chaotic dynamical system , 2003 .

[20]  Jinhu Lu,et al.  Synchronization of an uncertain unified chaotic system via adaptive control , 2002 .

[21]  Yuan Kang,et al.  Chaos in the Newton–Leipnik system with fractional order , 2008 .

[22]  Xiang-Jun Wu,et al.  Chaos in the fractional-order Lorenz system , 2009, Int. J. Comput. Math..

[23]  Vijay K. Yadav,et al.  Combined synchronization of time-delayed chaotic systems with uncertain parameters , 2017 .

[24]  Paul Woafo,et al.  Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design , 2018 .

[25]  Er-Wei Bai,et al.  Synchronization of two Lorenz systems using active control , 1997 .

[26]  Gamal M. Mahmoud,et al.  Double compound combination synchronization among eight n-dimensional chaotic systems , 2018, Chinese Physics B.

[27]  Ljupco Kocarev,et al.  General approach for chaotic synchronization with applications to communication. , 1995, Physical review letters.

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

[29]  Elena Grigorenko,et al.  Erratum: Chaotic Dynamics of the Fractional Lorenz System [Phys. Rev. Lett.91, 034101 (2003)] , 2006 .

[30]  Changpin Li,et al.  On chaos synchronization of fractional differential equations , 2007 .

[31]  Y. Kuramoto,et al.  Dephasing and bursting in coupled neural oscillators. , 1995, Physical review letters.

[32]  M. Lakshmanan,et al.  Chaos in Nonlinear Oscillators: Controlling and Synchronization , 1996 .

[33]  Yi Shen,et al.  Compound-combination anti-synchronization of five simplest memristor chaotic systems , 2016 .

[34]  M. Lakshmanan,et al.  SECURE COMMUNICATION USING A COMPOUND SIGNAL USING SAMPLED-DATA FEEDBACK , 2003 .

[35]  R. Leipnik,et al.  Double strange attractors in rigid body motion with linear feedback control , 1981 .

[36]  Tao Liu,et al.  A novel three-dimensional autonomous chaos system , 2009 .

[37]  Feiqi Deng,et al.  Double-compound synchronization of six memristor-based Lorenz systems , 2014 .

[38]  Vijay K. Yadav,et al.  Dual combination synchronization of the fractional order complex chaotic systems , 2017 .

[39]  Li-Peng Wang,et al.  Lag synchronization of chaotic systems with parameter mismatches , 2011 .

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

[41]  G. Tigan,et al.  Analysis of a 3D chaotic system , 2006, math/0608568.

[42]  Muhammad Rehan,et al.  Synchronization and anti-synchronization of chaotic oscillators under input saturation , 2013 .

[43]  Gheorghe Tigan,et al.  Heteroclinic orbits in the T and the Lü systems , 2009 .

[44]  Ivo Petras,et al.  Fractional-Order Nonlinear Systems , 2011 .