Synchronization, antisynchronization and amplitude death in coupled fractional order bistable oscillators

The dynamic behaviors of coupled fractional order bistable oscillators are investigated extensively and various phenomena such as synchronization, anti-synchronization, and amplitude death, etc. are explored. Based on the bistable characteristics of P-R oscillator with specific parameters, effects of initial conditions and coupling strength on the dynamic behaviors of the coupled fractional order bistable oscillators are first investigated by analyzing the maximum condition of Lyapunov exponent, the maximum Lyapunov exponent and the bifurcation diagram, etc. Further investigation reveals that the coupled fractional order bistable oscillators can be controlled to form chaotic synchronization, chaotic anti-synchronization, synchronous amplitude death, anti-synchronous amplitude death, partial amplitude death, and so on by changing the initial conditions and the coupling strength. Then, based on the principle of Monte Carlo method, by randomly choosing the initial conditions from the phase space, we calculate the percentage of various states when changing the coupling strength, so the dynamic characteristics of coupled fractional-order bistable oscillators can be represented by using the perspective of statistics. Some representative attractive basins are plotted, which are well coincident with numerical simulations.