Topology Affects Performance In Complex Dynamical Networks And Adaptive Chaos Synchronization

In order to design high performance artificial neural networks, in this paper, we compared the computational performance of the neural networks connected with regular lattice, random, small-world, and scale-free structures, and picked out the key characteristics.Motivated by the idea of adaptive control, we proposed a scheme for the synchronization, synchronization-based parameters identification and stabilization of neural networks with time-varying delay. Based on the combination of the adaptive strategy and linear feedback control, the adaptive scheme is proposed by dint of LaSalle invariance principle and Lyapunov functional method. The method proposed in this paper is quite robust against the effect of noise, and it can rapidly adjust its parameters to adapt the great changes in the operating parameters of the experimental system. The excellency of this scheme is well exhibited in numerical simulation.Concretely, the main results and originality of this paper are shown as follows:Firstly, in Chapter 2 we studied the computational performance of the neural networks connected with regular lattice, random, small-world, and scale-free structures. As graphs became less locally connected and more random, we found that the associative memory performance is well improved.Secondly, we proposed an adaptive scheme for the synchronization and stabilization of time-delayed neural networks with unknown parameters. In Chapter 3, by using LaSalle invariance principle and Lyapunov functional method, we studied the synchronization and stabilization of chaotic neural networks, and presented a synchronization-based parameters estimation method. In Chapter 4, the adaptive complete synchronization are presented for chaotic and hyperchaotic systems with fully unknown parameters.