Effective synchronization of a class of Chua's chaotic systems using an exponential feedback coupling

In this work a robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.Comment: 12 pages, 18 figure

Finite-time synchronization of tunnel diode based chaotic oscillators

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel diode based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulatioComment: 11 pages, 43 figure

Phase synchronization of bursting neural networks with electrical and delayed dynamic chemical couplings

Diffusive electrical connections in neuronal networks are instantaneous, while excitatory or inhibitory couplings through chemical synapses contain a transmission time-delay. Moreover, chemical synapses are nonlinear dynamical systems whose behavior can be described by nonlinear differential equations. In this work, neuronal networks with diffusive electrical couplings and time-delayed dynamic chemical couplings are considered. We investigate the effects of distributed time delays on phase synchronization of bursting neurons. We observe that in both excitatory and Inhibitory chemical connections, the phase synchronization might be enhanced when time-delay is taken into account. This distributed time delay can induce a variety of phase-coherent dynamical behaviors. We also study the collective dynamics of network of bursting neurons. The network model presents the so-called Small-World property, encompassing neurons whose dynamics have two time scales (fast and slow time scales). The neuron parameters in such Small-World network, are supposed to be slightly different such that, there may be synchronization of the bursting (slow) activity if the coupling strengths are large enough. Bounds for the critical coupling strengths to obtain burst synchronization in terms of the network structure are given. Our studies show that the network synchronizability is improved, as its heterogeneity is reduced. The roles of synaptic parameters, more precisely those of the coupling strengths and the network size are also investigated