Anti-coherence and coherence resonance induced by nonlinear time delay in autonomous stochastic system

An autonomous stochastic system with nonlinear time-delayed feedback is investigated employing the stochastic simulation method. In the autonomous stochastic system with quadratic time-delayed feedback or under positive feedback, the nonlinear delay time fails to possess the role improving the noisy state of the system. In the autonomous stochastic system with cubic time-delayed feedback and under negative feedback, the nonlinear delay time can improve the noisy state, tuning the signal output, and generating incoherence and coherence maximization. We reveal a new kind of anti-coherence and coherence resonance phenomena induced by the nonlinear time delay in the autonomous stochastic system without external periodic force, discussing further the effects of the noise strength, the control parameter, and the feedback strength on anti-coherence and coherence resonance