Chaotic Synchronization Of Several Regular Nonlinear Networks And It's Application

In recent decade, chaos control and chaos synchronization are among the key points for the chaos application in nonlinear networks. Therefore, the synchronization concept in the Huygens age, which is only related to various kinds of frequency-locking or phase-locking of periodic motions, has been extended to a variety of chaotic systems, including complete synchronization, generalized synchronization, phase synchronization, lag synchronization, partial synchronization, etc. Thus, some new questions about the synchronization-desynchronization bifurcation, the construction of nonlinear networks and the study of it's dynamics have been put forward. We introduce the latest development and corresponding studying fruits on nonlinear networks in the 1st chapter.In the 2nd chapter, we investigate the dynamic instabilities of ring and linear arrays of chaotic oscillators with asymmetric nearest-neighbor couplings. Based on the master stability function (MSF) and eigenvalue analysis (EA), we give the semi-analytical relations between the critical values and the coupling constants. Results are demonstrated with numerical simulations in a set of coupled Lorenz oscillators.In the 3rd chapter, we study the dynamics of uni-directionally coupled linear arrays of chaotic oscillators in star configuration, and find a new kind of synchronization - layered synchronization, which severely depends on the dynamical coupling symmetry. Numerically calculation shows that, for Lorenz oscillator, the strange attractor spiralling around two focus points will become the strange attractor spiralling around one focus point down the linear arrays. The stabilities of the synchronized states are enhanced by chaos, and degraded when the oscillators are far from the central driving oscillator.In the 4th chapter, based on the layered chaotic synchronization, we propose a new secure communication scheme. In this scheme, because we can randomly select different high-dimensional chaotic signals to mask the message in different time interval during communication, and simultaneously transmit the selection information (which chaotic oscillators are selected?) to receiver through public channel, the communication security is enhanced. Furthermore, the dynamical symmetry between the transmitting and receiving systems prevent the attacker getting signal from the channel.In the 5th chapter, stable propagation of noise-induced synchronous spiking in uncoupled linear neuron arrays is studied numerically. The chaotic neurons in the uni-directionally coupled linear array are modeled by Hindmarsh-Rose neurons. Stability analysis shows that the synchronous chaotic spiking can be successfully transmitted to cortical areas through layered synchronization in the neural network under certain conditions of the network structure.