Stochastic Dynamical Behaviors for a Time-Delayed Insect Outbreak System with a Periodic Signal Subjected to Multiplicative and Additive Noises

Abstract

In this paper, our aim is to investigate the steady state behaviors, the stochastic resonance (SR) phenomenon and the mean decline time for a biological insect growth system induced by the terms of time delay, the multiplicative and additive noises. Numerical results indicate that the multiplicative noise and the additive one can both weaken the stability of the biological system and accelerate the depression process of the insect population, while time delay can strengthen the stability of the insect growth system and prolong the lifetime of the insect system. With respect to the SR phenomenon caused by time delay, noise terms and the weak periodic signal, the results show that some interesting dual peak phenomena for the signal-to-noise ratio (SNR) occur frequently. Specific contents are as follows: In SNR-[Formula: see text] plots, the additive noise intensity [Formula: see text] and time delay [Formula: see text] can easily induce the phenomenon of dual peaks, while in the SNR-[Formula: see text] plots, the multiplicative noise intensity [Formula: see text] and time delay [Formula: see text] can both reduce the SR effect distinctly. On the other hand, in the SNR-[Formula: see text] plots, when either of [Formula: see text] or [Formula: see text] takes a big value, the other plays a negative role in stimulating the SR phenomenon; while either of them takes a small value, the other can excite a significant effect of double peaks.