Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method

This article deals with the anti-synchronization between two identical chaotic fractional-order Qi system, Genesio–Tesi system, and also between two different fractional-order Genesio–Tesi and Qi systems using active control method. The chaotic attractors of the systems are found for fractional-order time derivatives described in Caputo sense. Numerical simulation results which are carried out using Adams–Boshforth–Moulton method show that the method is reliable and effective for anti-synchronization of nonlinear dynamical evolutionary systems.

[1]  Mohd. Salmi Md. Noorani,et al.  Anti-synchronization of chaotic systems with uncertain parameters via adaptive control , 2009 .

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

[3]  S. S. Yang,et al.  Generalized Synchronization in Chaotic Systems , 1998 .

[4]  E. M. Shahverdiev,et al.  Lag synchronization in time-delayed systems , 2002 .

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

[6]  Jinhu Lü,et al.  Stability analysis of linear fractional differential system with multiple time delays , 2007 .

[7]  Alan D. Freed,et al.  Detailed Error Analysis for a Fractional Adams Method , 2004, Numerical Algorithms.

[8]  M. T. Yassen,et al.  Chaos synchronization between two different chaotic systems using active control , 2005 .

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

[10]  Varsha Daftardar-Gejji,et al.  Analysis of a system of fractional differential equations , 2004 .

[11]  M. Noorani,et al.  Adaptive reduced-order anti-synchronization of chaotic systems with fully unknown parameters , 2010 .

[12]  P. Balasubramaniam,et al.  Synchronization of chaotic systems under sampled-data control , 2012 .

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

[14]  J Kurths,et al.  Phase synchronization in time-delay systems. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  B. Onaral,et al.  Linear approximation of transfer function with a pole of fractional power , 1984 .

[16]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[17]  Tieshan Li,et al.  Adaptive terminal sliding mode control for anti-synchronization of uncertain chaotic systems , 2013 .

[18]  Zuo-Lei Wang,et al.  Anti-synchronization of Liu system and Lorenz system with known or unknown parameters , 2009 .

[19]  Jinghua Xiao,et al.  Antiphase synchronization in coupled chaotic oscillators. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Santo Banerjee,et al.  Adaptive synchronization in noise perturbed chaotic systems , 2012 .

[21]  I. Podlubny.  Fractional differential equations , 1998 .

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

[23]  M. Ichise,et al.  An analog simulation of non-integer order transfer functions for analysis of electrode processes , 1971 .

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

[25]  Tao Yang.  Control of Chaos Using Sampled-Data Feedback Control , 1998 .

[26]  Meng Zhan,et al.  Complete synchronization and generalized synchronization of one-way coupled time-delay systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Pagavathigounder Balasubramaniam,et al.  Synchronization of recurrent neural networks with mixed time-delays via output coupling with delayed feedback , 2012, Nonlinear Dynamics.

[28]  Pagavathigounder Balasubramaniam,et al.  Chaotic synchronization of Rikitake system based on T-S fuzzy control techniques , 2013 .

[29]  Hongjie Yu,et al.  Chaotic synchronization based on stability criterion of linear systems , 2003 .

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

[31]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[32]  Zhi-Hong Guan,et al.  Adaptive synchronization between two different hyperchaotic systems , 2008 .

[33]  Subir Das,et al.  Synchronization between fractional-order Ravinovich–Fabrikant and Lotka–Volterra systems , 2012 .

[34]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[35]  M. Noorani,et al.  Adaptive anti-synchronization of two identical and different hyperchaotic systems with uncertain parameters , 2010 .

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

[37]  Yang Yang,et al.  Chaos in the Fractional-Order Qi System and Its Synchronization Using Active Control , 2010, 2010 International Conference on Intelligent Computing and Cognitive Informatics.

[38]  Mohd. Salmi Md. Noorani,et al.  Active Anti-Synchronization of two Identical and Different Fractional-Order Chaotic Systems , 2011 .

[39]  N. Laskin.  Fractional market dynamics , 2000 .

[40]  Jun-an Lu,et al.  Parameter identification and backstepping control of uncertain Lü system , 2003 .

[41]  R. Koeller.  Applications of Fractional Calculus to the Theory of Viscoelasticity , 1984 .

[42]  D. Kusnezov,et al.  Quantum Levy Processes and Fractional Kinetics , 1999, chao-dyn/9901002.

[43]  E. Ahmed,et al.  Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models , 2007 .

[44]  Jianbo Liu,et al.  Anti-phase synchronization in coupled map lattices , 2000 .

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

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

[47]  Hadi Delavari,et al.  Chaos in fractional-order Genesio–Tesi system and its synchronization , 2012 .

[48]  Ju H. Park,et al.  A novel criterion for delayed feedback control of time-delay chaotic systems , 2005 .

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

[50]  Yinping Zhang,et al.  Chaotic synchronization and anti-synchronization based on suitable separation , 2004 .

[51]  Shihua Chen,et al.  Adaptive control for anti-synchronization of Chua's chaotic system , 2005 .

[52]  Hadi Taghvafard,et al.  Numerical solution of the high thermal loss problem presented by a fractional differential equation , 2011 .

[53]  Kai Diethelm,et al.  Multi-order fractional differential equations and their numerical solution , 2004, Appl. Math. Comput..

[54]  H. Yau.  Design of adaptive sliding mode controller for chaos synchronization with uncertainties , 2004 .

[55]  Lilian Huang,et al.  Synchronization of chaotic systems via nonlinear control , 2004 .

[56]  K. Shore,et al.  Inverse anticipating chaos synchronization. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  S. Bhalekar,et al.  Antisynchronization of Nonidentical Fractional-Order Chaotic Systems Using Active Control , 2011 .