Statistical Study On Time-delay Foraging System Driven By Internal And External Noise

Stochastic interference can lead to the transformation of ecosystem homeostasis from one state to another,which may lead to changes in the structure of the ecosystem.At present,researchers consider the effect of non-Gaussian noise on ant feeding system,and study the effect of single noise on foraging population system.Therefore,we study the statistical properties of time-delay foraging systems driven by internal and external noise.Based on foraging population model,the stationary probability distribution?SPD?expression of foraging system is derived by means of the small time delay and markov ap-proximation,the effects of noise and delay parameter changes on the steady-state changes and dynamic characteristics of foraging system are mainly studied.Next,the mean first pass time?MFPT?from metastable to steady state is discussed,and the effects of noise and delay on MFPT are investigated.The probability distribution function?PDF?of the first pass time?FPT?was finally investigated to further understand the effects of noise and delay on transient characteristics of foraging systems.The following conclusions were drawn:?1?the time delay and noise can lead to bistable spontaneous generation for ant-eating population models.From the SPD point of view,it can be seen that with the increase of external noise intensity D and non-gaussian noise deviation parameter q,the structure of SPD changes from single peak to double peak,whereas with the increase of noise intensity?,the structure changes from double peak to single peak,that is,noise leads to ant transition between different states.?2?With the change of noise intensity?,the MFPT presents a maximum value,which is expressed as the noise-enhancing stabili-ty?NES?effect is generated in the foraging system.In addition,the MFPT also presents a maximum with the change of time delay?and correlation time?₀,indicating that the delayed enhancement stability?DES?effect occurs.Thus,the noise and delay can enhance the stability of the foraging system.?3?The peak value decreases and starts to shift to the left as the noise parameters?,D and q increase,which indicates that the probability of ant transition to food source is the highest at a certain time and the transition time between different states gradually decreases;the curve gradually shifts to the right as the correlation time?₀increases,indicating that larger?₀and?increases the time required for ant transition.