The Study Of Time Delay Effects For Regime Shifts In Insect Ecosystem Under Stochastic Disturbance

In this paper,the stochastic and delay effects of insect ecosystem were investigat-ed.Combination of noises and time delays can have distinct and complex influences in the insect outbreak system.A deeper understanding of combination between noises and time delays interacts with nonlinearity,will lead to important new insights in population ecology,and may provide some theoretical intuitions for real insect ecosystems.Next,the related stochastic and delay theory are introduced.Bases on stationary probability densi-ty(SPD),mean first passage time(MFPT)and signal-to-noise ratio(SNR),we analyzed the effect of noise strength and time delay in classical budworm ecological model of insec-t dynamics system by method of small time delay approximation theory,the following results show:1.considering time delays in the deterministic and stochastic forces,we construct stochastic delayed differential equations to investigate the regime shifts in an insect e-cosystem.The stationary probability distribution(SPD)and mean first passage time(MFPT)are obtained,respectively.Our main results show:(i)The multiplicative noise,positive cross-correlation noise between two noises and time delays can induce the regime shifts from the boom outbreak state to the bust one,but the additive noise and negative cross-correlation can induce the regime shifts from the bust outbreak state to the boom one;(ii)For the negative cross-correlation,the MFPT as a function of noise strengths exhibits one maximum,at which shows the characteristic of the noise-delayed switching for the boom outbreak state,but for the no cross-correlation or positive cross-correlation,the MFPT decreases with the noise strengths;(iii)Two different types of time delays play same roles on the maximal MFPT with additive noise,and play opposite roles on the maximal MFPT with multiplicative noise.The mechanisms for noises-and delays-induced regime shifts between two states can be explained physically through the effective potential of ecological model.2.considering additive and multiplicative periodic signals,we have investigated the stochastic resonance(SR)phenomenon in an insect ecosystem with two different types of time delays,at which the insect dynamics is assumed to be disturbed by both additive and multiplicative noises.The signal-to-noise ratio(SNR)is calculated when two different weak periodic signals are added to the insect system.It is shown from the SNR that the additive and multiplicative periodic signals can cause the SR and double SR in the case of time delays in the stochastic and deterministic force,respectively.A detailed study of the SNR depending on various noise characteristics is performed,and the main results about SR are compared for two different cases of time delays.In short,different types of noises and time delays can induce the regime shifts be-tween the boom and bust outbreak state,the presences of noises and time delays reveals an influence of additional feature in the deterministic insect ecosystem.In addition,com-bination of different noises and time delays can have distinct and complex impacts for the resonance phenomenon,and may provide some theoretical intuitions for real insect e-cosystems,and offer some method to analyze some complex stochastic delayed differential equations.Therefore,we expect these analysis will stimulate theoretical and experimental works to verify that influences of time delay in population ecological systems.