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

This paper investigates the stochastic resonance (SR)phenomenon induced by the multiplicative periodic signal in a cancergrowth system with the cross-correlated noises and time delay. Todescribe the periodic change of the birth rate due to the periodictreatment, a multiplicative periodic signal is added to the system.Under the condition of small delay time, the analytical expressionof the signal-to-noise ratio R_{rm SNR} is derived in theadiabatic limit. By numerical calculation, the effects of thecross-correlation strength lambda and the delay time tau onR_{rm SNR} are respectively discussed. The existence of a peak inthe curves of R_{rm SNR} as a function of the noise intensitiesindicates the occurrence of the SR phenomenon. It is found thatlambda and tau play opposite role on the SR phenomenon, i.e.,the SR is suppressed by increasing lambda whereas it is enhancedwith the increase of tau, which is different from the case wherethe periodic signal is additive.