Abstract
Nonlocal coupling, as an important connection topology among nonlinear oscillators, has attracted increasing attention recently with the research boom of chimera states. So far, most previous investigations have focused on nonlocally coupled systems interacted via similar variables. In this work, we report the evolutions of dynamical behaviors in the nonlocally coupled Stuart–Landau oscillators by applying conjugate variables feedback. Through rigorous analysis, we find that the oscillation death (OD) can convert into the amplitude death (AD) via the cluster state with the increasing of coupling range, making the AD regions to be expanded infinitely along two directions of both the natural frequency and the coupling strength. Moreover, the limit cycle oscillation (OS) region and the mixed region of OD and OS will turn to anti-synchronization state through amplitude-mediated chimera. Therefore, the procedure from local coupling to nonlocal one implies indeed the continuous enhancement of coherence among neighboring oscillators in coupled systems.
Highlights
The investigation of coupled nonlinear oscillators model creates a favorable and effective platform for exploring various oscillatory patterns in physics, chemistry and neuroscience
Thenceforth, nonlocal coupling topology has often been considered as a necessary condition to induce chimera states, and different types of chimera states have been discovered in nonlocally coupled models, such as, amplitude-mediated chimera[26,27], and pure amplitude chimera and chimera death[28,29]
Let us consider a ring of N identical nonlocally coupled Stuart-Landau oscillators, and the oscillators are coupled mainly through conjugate variables, the dynamic equation is shown as
Summary
Let us consider a ring of N identical nonlocally coupled Stuart-Landau oscillators, and the oscillators are coupled mainly through conjugate variables, the dynamic equation is shown as. Where i = 1, 2, ..., N, the parameter ε denotes the coupling strength, and w is the inherent frequency of the oscillators. Nonlocally coupled oscillators (Eq (1)) are solved numerically by the fourth order Runge-Kutta method with integration step size h = 0.01, and the initial condition is adopted as follows: the former 50 oscillators are specified to start from positive constants In the following we consider firstly the generation condition of AD through executing linear stability analysis method, and the Jacobian matrix J at the origin can be obtained as follows:
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