Coherence resonance induced by time delay in autonomous system

An autonomous system of a two-dimensional model driven by noise with time-delayed feedback is investigated employing stochastic simulation. We show evolution of the dynamic variables with time, and present the distribution graphs of the power spectrum and the peak frequency. Time delay can switch the system from a noisy state to a regular stage state, creating peaks in the spectrum distribution, changing the period, and shifting the peak frequency of the power spectrum. By analysis, we reveal the coherence resonance phenomenon induced by the time delay without external periodic force. Using the criterion of coherent resonance, we discuss further the effects of the time delay, the feedback strength, the noise strength, and the control parameter for coherence resonance.