Coherence of a periodic potential system with nonlinear nonlocal dissipation and colored noise

The coherence of a periodic potential system with memory kernel is studied under the action of nonlinear dissipation and colored noise. General expression for the characteristic correlation time is derived for a multi-stable discrete rate process describing the noise-induced transition between states. The coherence can be improved by the strength of memory, while it is shown to be minimized for an appropriate choice of the modulation parameter of dissipation and the number of stable states. Moreover, the phenomena of coherence resonance, anti-coherence resonance, and stochastic multi-resonance are found by simulating quality factor as the memory of the dynamical system is unrelated to its noise spectrum. Specifically, the noise correlation time and the memory time play remarkably different roles in an enhancement of coherence resonance. The quality factor also exhibits a resonance-like dependence on the friction coefficient. More interestingly, in certain parameter regions a scheme for controlling coherence resonance can be achieved by introducing nonlinear dissipation.