Influence of Time Delay on Stochastic Resonance in the Tumor Cell Growth Model

Abstract

We study the effects of time delay on stochastic resonance (SR) in the tumor cell growth model driven by two coupled noises and a weak external periodic signal. Under the condition of small delay time, we obtained the signal-to-noise ratio (SNR) R SNR from the quasi-steady-state probability distribution function through the adiabatic elimination method and the SR theory about a two-state transition. By the numerical computations, we discussed the effects of the delay time τ on the SNR as a function of the multiplicative noise intensity D, the additive noise intensity α and the cross-correlated strength λ respectively. The appearance of a peak in these curves represents the SR phenomenon. It is found that with the increase of τ, the SR is suppressed in the D–R SNR plot and weakened in the α–R SNR plot. However, the SR is strengthened with the increase of τ in the λ–R SNR plot.

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

“…In most practically relevant cases, the state of the system should be affected in the first place by its immediate past, with additional correction arising from the time delay [37][38][39][40]. After introducing a time delay into the tumor cell growth model, one obtains:…”

“…Such a kernel is equivalent to a time delay [35,36]. In practice, in many physical as well as biological systems, time delays always exist and play a significant role in the dynamics of the system [37][38][39][40]. Well-known examples include biophysiological controls [41], neuronal networks [42] , and optical cavities [43,44].…”

Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system

“…One should note that the effect of the delay time on the SR is different from the case of the additive signal, in which the SR is weakened by increasing the delay time. [25] The SNR R SNR as a function of the additive noise intensity D is respectively plotted in Figs. 3 and 4, for different values of the cross-correlation strength λ and the delay time τ .…”

“…Many studies have been devoted to the effects of noise on the time-delayed systems, and have shown that the combination of noise and time delay fundamentally changes the statistical properties of the systems. [23,24] Particularly, the effect of time delay on the SR has been investigated in different time-delayed stochastic systems, which revealed that the time delay has important influence on the SR. [25,26] The analytical approximate method for time-delayed stochastic systems has been developed for the case of small delay time. [22] When the delay time is large, the numerical simulation method can be used.…”

Impact of two types of time delays and cross-correlated multiplicative and additive noises on stability and stochastic resonance for a metapopulation system

“…In fact, dynamical characteristics occurred in many monostable or bistable dynamical systems are accompanied with memory, which is in most cases equivalent to a time delay [17][18] . In practice, in many physical as well as biological systems, time delays always exist and play a significant role in the dynamics of the system [19][20][21][22] . Well-known examples can be found in biophysiological controls [23] , neuronal networks [24] , and optical cavities [25][26] .…”