Study on entrainment and chaos in coupled qualitatively different oscillators

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Present research was mainly devoted to the subject of elucidating the effect of increasing the ratio of inactive elements (damped oscillators) in globally and diffusively coupled oscillators. Main results are as follows :1.Aging transitionWe found by taking coupled Stuart-Landau(SL) oscillators and coupled Roessler systems as examples that when the coupling strength K is larger than a threshold value, the system stops oscillation at a value of the ratio of inactive elements, p, which is less than one : p<1.2.Universal scaling at the aging transitionOscillation amplitude of the centroid of the system, which was introduced as an order parameter of the aging transition, was shown to obey universal scaling laws at the transition.3.Desynchronization horn - violation of the synchronization of active oscillators -Active oscillators were found to desynchronize and form clusters in a horn-like region of the (K,p) phase diagram, provided that the nonisochronicity of oscillators is sufficiently strong. This phenomenon was analyzed in detail for coupled SL oscillators.4.Diffusion-induced inhomogeneity - Swing-by mechanism -The mechanism was identified by which increasing the value of K leads to an enhancement of the system's inhomogeneity in the desynchronization horn. Moreover, a theory was presented to predict for what value of K the system becomes most inhomogeneous.5.An experimental method to measure phase order parametersIn collaboration with a Virginia university group, a method was proposed to measure phase order parameters of a large population of oscillators using only data of one macroscopic quantitiy. This method remains to be extended to aged systems.