Abstract
The effects of the initial conditions and the coupling competition modes on the dynamic behaviors of coupled non-identical fractional-order bistable oscillators are investigated intensively and the various phenomena are explored. The coupled system can be controlled to form chaos synchronization, chaos anti-phase synchronization, amplitude death, oscillation death, etc., by setting the initial conditions or selecting the coupling competition modes. Depending on whether the arbitrary initial conditions can let two coupled oscillators stop oscillating, the dynamic behaviors of the coupled system are further classified into three types, that is, both of oscillators stop oscillating, only one oscillator stops oscillating, and none of oscillators stop oscillating. Based on the principle of Monte Carlo method, the percentages of three types of dynamic behaviors are calculated for the different coupling competition modes and the dynamic behaviors of the coupled system are characterized from the perspective of statistics. Moreover, the mechanism behind the various phenomena is explained in detail by the concept of boundary layer and the optimum coupling competition modes are found.
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