Chaos and its synchronization in two-neuron systems with discrete delays

作者: Shangbo Zhou , Xiaofeng Liao , Juebang Yu , Kwok-wo Wong

DOI: 10.1016/J.CHAOS.2003.10.031

关键词: Synchronization of chaosSynchronization (computer science)CorrectnessLyapunov exponentCHAOS (operating system)MathematicsControl theoryCommunications systemControl of chaosDimension (vector space)

摘要: Abstract It is well known that complex dynamic behaviors exist in time-delayed neural systems. Infinite positive Lyapunov exponents can be found chaotic systems since the dimension of such infinite. However, theoretical and experimental models studied thus far are low dimensional with only one exponent. Consequently, messages masked by shown to easily extracted some cases. Therefore, communication system a higher security level design means neuron In this paper, we firstly investigate dynamical two-neuron discrete delays. Then, chaos synchronization based on method designing coupled employing Krasovskii–Lyapunov theory search conditions. Numerical results illustrate correctness our analyses.

参考文章(14)
Rong He, P. G. Vaidya, Time delayed chaotic systems and their synchronization Physical Review E. ,vol. 59, pp. 4048- 4051 ,(1999) , 10.1103/PHYSREVE.59.4048
Michael G. Rosenblum, Arkady S. Pikovsky, Jürgen Kurths, Phase synchronization of chaotic oscillators Physical Review Letters. ,vol. 76, pp. 1804- 1807 ,(1996) , 10.1103/PHYSREVLETT.76.1804
Louis M. Pecora, Thomas L. Carroll, Synchronization in chaotic systems Physical Review Letters. ,vol. 64, pp. 821- 824 ,(1990) , 10.1103/PHYSREVLETT.64.821
Xiaofeng Liao, Kwok-Wo Wong, Chi-Sing Leung, Zhongfu Wu, Hopf bifurcation and chaos in a single delayed neuron equation with non-monotonic activation function Chaos Solitons & Fractals. ,vol. 12, pp. 1535- 1547 ,(2001) , 10.1016/S0960-0779(00)00132-6
Ömer Morgül, Moez Feki, A chaotic masking scheme by using synchronized chaotic systems Physics Letters A. ,vol. 251, pp. 169- 176 ,(1999) , 10.1016/S0375-9601(98)00868-8
Boualem Mensour, André Longtin, Synchronization of delay-differential equations with application to private communication Physics Letters A. ,vol. 244, pp. 59- 70 ,(1998) , 10.1016/S0375-9601(98)00271-0
Gabriel Pérez, Hilda Cerdeira, Extracting Messages Masked by Chaos Physical Review Letters. ,vol. 74, pp. 1970- 1973 ,(1995) , 10.1103/PHYSREVLETT.74.1970
M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phase synchronization in driven and coupled chaotic oscillators IEEE Transactions on Circuits and Systems I-regular Papers. ,vol. 44, pp. 874- 881 ,(1997) , 10.1109/81.633876
M.J. Ogorzalek, Taming chaos. I. Synchronization IEEE Transactions on Circuits and Systems I-regular Papers. ,vol. 40, pp. 693- 699 ,(1993) , 10.1109/81.246145
K. Pyragas, SYNCHRONIZATION OF COUPLED TIME-DELAY SYSTEMS : ANALYTICAL ESTIMATIONS Physical Review E. ,vol. 58, pp. 3067- 3071 ,(1998) , 10.1103/PHYSREVE.58.3067