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.
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