Chaotic synchronization of a fractional neuron network system with time-varying delays

Chaos in a fractional-order neuron network system with varying time delays is illustrated. Chaotic synchronization system for such system is constructed. The theoretic analyses are given by Laplace transformation theory, the bifurcation graph with respect to coupled parameter is presented, and the numerical experiments are presented. The study shows that the chaos in such fractional-order neuron networks with varying time delay can be synchronized. Furthermore, several different coupled systems are constructed, and the synchronization characteristics are compared.

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

[2]  Allan K. Evans,et al.  The Effects of Continuously Varying the Fractional Differential Order of Chaotic Nonlinear Systems , 1999 .

[3]  P. Arena,et al.  Chaotic behavior in noninteger-order cellular neural networks , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Kwok-Wo Wong,et al.  Chaos and its synchronization in two-neuron systems with discrete delays , 2004 .

[5]  Dov Ingman,et al.  Control of damping oscillations by fractional differential operator with time-dependent order , 2004 .

[6]  Yangquan Chen,et al.  Fractional Calculus and Biomimetic Control , 2004, 2004 IEEE International Conference on Robotics and Biomimetics.

[7]  Xiaohua Xiong,et al.  Extending synchronization scheme to chaotic fractional-order Chen systems , 2006 .

[8]  Julien Clinton Sprott,et al.  Chaos in fractional-order autonomous nonlinear systems , 2003 .

[9]  Shangbo Zhou,et al.  Chaos control and synchronization in a fractional neuron network system , 2008 .

[10]  Shangbo Zhou,et al.  Chaos and Synchronization of Time-Delayed Fractional Neuron Network System , 2008, 2008 The 9th International Conference for Young Computer Scientists.

[11]  M. Alper Kutay,et al.  The Fractional Fourier Transform and Harmonic Oscillation , 2002 .

[12]  Reyad El-Khazali,et al.  Identification of fractional chaotic system parameters , 2004 .

[13]  Daolin Xu,et al.  Chaos synchronization of the Chua system with a fractional order , 2006 .

[14]  Ingo Schäfer,et al.  Fractional Calculus via Functional Calculus: Theory and Applications , 2002 .

[15]  Y. Chen,et al.  Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives—an Expository Review , 2004 .

[16]  Yaolin Jiang,et al.  Generalized projective synchronization of fractional order chaotic systems , 2008 .

[17]  Ahmad Harb,et al.  On nonlinear control design for autonomous chaotic systems of integer and fractional orders , 2003 .

[18]  P. Arena,et al.  Bifurcation and Chaos in Noninteger Order Cellular Neural Networks , 1998 .

[19]  Naser Pariz,et al.  A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter , 2009 .

[20]  Wei-Ching Chen,et al.  Nonlinear dynamics and chaos in a fractional-order financial system , 2008 .

[21]  G. H. Erjaee,et al.  Phase synchronization in fractional differential chaotic systems , 2008 .

[22]  Reyad El-Khazali,et al.  Stabilization of generalized fractional order chaotic systems using state feedback control , 2004 .

[23]  J. A. Tenreiro Machado,et al.  Chaotic Phenomena and Fractional-Order Dynamics in the Trajectory Control of Redundant Manipulators , 2002 .

[24]  Tom T. Hartley,et al.  Fractional-order system identification based on continuous order-distributions , 2003, Signal Process..

[25]  Junguo Lu,et al.  CHAOTIC DYNAMICS AND SYNCHRONIZATION OF FRACTIONAL-ORDER CHUA'S CIRCUITS WITH A PIECEWISE-LINEAR NONLINEARITY , 2005 .

[26]  Wajdi M. Ahmad.  Generation and control of multi-scroll chaotic attractors in fractional order systems , 2005 .