Stochastic resonance induced by the memory of a random delay

Abstract

We study the stochastic resonance (SR) induced by the memory of a random delay in a bistable system driven by a periodic force. Resorting to numerical simulations, we first analyze the stochastic bifurcation diagram and find that the jump of a Brownian particle between two potential wells becomes regular and exhibits strong periodicity at some optimal noise level. On the other hand, from the viewpoint of signal-to-noise ratio (SNR) theory, we find that the SNR curves vary non-monotonically and behave as an obvious SR phenomenon. Moreover, the parameter-tuning stochastic resonances about the system parameters are also investigated in this paper.

Stationary distribution extinction and optimal control for the stochastic hepatitis B epidemic model with partial immunity

“…with maximality and transversality conditions * * ( ) for the control problem ( 10)- (12). Then, there exist an model of adjoint…”

“…We analytically solved the control problem for the control and state variables by providing the adjoint equations (23) and its associated conditions (12) and (24) as well as characterization of the control measures. Next, we will study the control theory of the stochastic system (stochastic variant of model (1)) while implementing the same control measures.…”

“…Researches of different areas from the very beginning are trying to finish the infectious diseases or to stabilize them up to some degrees. The researchers of mathematics also provide their contribution in the investigation of different dynamical systems related to infectious diseases (see e.g., [9][10][11][12]). In the recent time mathematical models of various epidemiology or infectious diseases have been made for the investigation of optimal control and stabilities of the concerned problems.…”

Generalized stochastic resonance in a linear fractional system with a random delay

“…Here the delay, used to model the feedback time, should be random due to the heterogeneity of the medium. To the best of our knowledge, although mathematical models for random delays have been considered in the literature [12], [22]- [24], little attention has been paid to the stochastic resonance phenomena of the random-delayed systems.…”