Synchronization And Oscillation Death In Coupled Non-Identical Nonlinear Oscillators

Rich dynamics of the chaotic systems had been explored and revealed by the researchers since great efforts had been stress on the nonlinear dynamics reasearch. Rich collective dynamics had been found in the coupled chaotic oscillators such as various of synchronization and the oscillation death which are formed by the interaction between the coupled units with parameter mismatches or time delay. It is significant to explore these dynamics for its perspective applications in chaos control and security communications. In this article, the collective dynamics such as the synchronization and the oscillation death in a ring of coupled non-identical nonlinear oscillators are explored in detail especillay on the effects of the spatial distribution of parameters.In the first chapter, the background and theories of the nonlinear dynamics system are introduced which will be applied in the following discussions.In the second chapter, the effects of spatial distribution of coupling strength on the synchronizability are explored in a ring of diffusively coupled identical oscillators. We find that the inhomogeneity coupling strengths with different spatial arrangements have great impacts on the synchronizability of a ring of diffusively coupled oscillators. Base on the master stability function method, the second largest eigenvalues (λ2) of the coupling matrixes are calculated for all possible spatial arrangements of coupling strengths.λ2which can describe the synchronizability of coupled oscillators, are found obeying a log-normal distribution. When the spatial arrangement of coupling strength is in period1(2) state, the value of λ2is the smallest(largest) which indicate that the arrangement of period1has the best synchronizability while that of period2has the worst one. In addition, the regimes of the effects of spatial distribution on synchronizability are analyzed by taking a ring of coupled Rossler systems as an example. The effects of the parameter arrangements on the collectively dynamics have meaningful the applications in the manipulation of the self-organization dynamics of the coupled systems.In the third chapter, the effect of spatial frequencies distributions on the oscillation death in a ring of coupled nonidentical oscillators is studied. We find that the rearrangement of the spatial frequencies may deform the domain of parameters of the oscillation death. The usual critical curves with shape V in the parameter spaces of frequency-mismatch versus coupling-strength may become the shape W (or even shape WV). A kind of ragged oscillation death is observed for some spatial arrangements. The theoretical analyses are presented to predict the ragged oscillation death and the consistent of numerically observed in coupled nonidentical nonlinear dynamics.In the fourth chapter, the effect of the spatial frequencies distributions on the efficiency of phase synchronization are explored in an array of coupled oscillators with diverse natural frequencies distributions. A universal log-normal distribution of critical coupling strength Kc for phase synchronization is found. Moreover, the effciencies of the phase synchronization increases non monotonousily with the roughness of the spatial configuration of the frequencies.In the fifth chapter, the summary of the whole articles are present.