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

Abstract

Abstract:The phenomenon of stochastic resonance (SR) in a tumor growth model under the presence of immune surveillance is investigated. Time delay and cross-correlation between multiplicative and additive noises are considered in the system. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced multiplicatively. Our results show that: (i) the time delay can accelerate the transition from the state of stable tumor to that of extinction, however the correlation between two noises can accelerate the transition from the state of extinction to that of stable tumor; (ii) the time delay and correlation between two noises can lead to a transition between SR and double SR in the curve of SNR as a function of additive noise intensity, however for the curve of SNR as a function of multiplicative noise intensity, the time delay can cause the SR phenomenon to disappear, and the cross-correlation between two noises can lead to a transition from SR to stochastic reverse-resonance. Finally, we compare the SR phenomenon for the multiplicative periodic signal with that for additive periodic signal in the tumor growth model with immune surveillance. PACS

Stochastic resonance and stability for a time-delayed cancer growth system subjected to multiplicative and additive noises

“…In particular, the time delay τ can even make the tumor cells go into extinction. In other words, it is found that a weak Finally, the results in the present paper and the ones in [38] are compared. The stochastic tumor model is written as x…”

“…ω Nevertheless, [38] considers the case of the negative multiplicative periodic signal A t cos( ). the term of time delay in [38] is x t x t ( ) ( ).…”

“…ω Nevertheless, [38] considers the case of the negative multiplicative periodic signal A t cos( ). the term of time delay in [38] is x t x t ( ) ( ). θ τ − All of these factors lead to the vast disparity of the physical characteristics for the SNR between the two articles.…”

“…There are a lot of nonlinear stochastic systems with timedelayed feedback, and by which, the signals or other key quantities of the systems are fed back from output interfaces. In order to investigate the crucial role of time delay upon the SR phenomenon, research has been recently extended to the time-delayed systems that are subjected to multiplicative and additive noises [11][12][13][14][35][36][37][38][39][40][41][42]. For the case of a small delay time, the analytical approximation method for time-delayed stochastic systems has been developed [15], and in the case that the time delay is large, a numerical simulation method can be used [16].…”

Gaussian and Lévy noises excited delayed tumor growth model: first-passage behavior and stochastic resonance

“…For a long time in the past, the study of dynamical systems has often ignored the inherent time delay in the system, and with the ever-increasing requirements for system accuracy, the effect of time delay on the system is becoming more and more non-negligible. Biologically, the proliferation process of tumor cells does not occur instantaneously, and the periodic treatment is not immediate, so the effect of time delay should be considered when studying the growth process of tumor cells [44][45][46][47][48][49]. Alberto et al [46] investigated the stability and Hopf bifurcation of the immobile point of a delayed tumor growth model.…”