The Research Of Dynamic Behaviors Of Population With Allee Effect Induced By Non-gaussian Noise

Population is the basic unit of biological evolution and an important component of ecosystem.The growth of the population is an important indicator of the ecological balance.Recently,the study of population growth has attracted extensive attention and discussion in the academic community.It has great significance to maintain the stability and balance of ecosystems by establishing a population model with Allee effect,especially for the study of population models affected by environmental disturbances.It provides new ideas and methods for maintaining ecological balance,protecting biodi-versity and regulating interspecific relationships.In this paper,we explored the effects of environmental noise and Allee effect on the stationary probability distribution and mean first-passage time based on the single species population model with Allee effect.The main contents and conclusions are summarized as follows:1.The dynamic behaviors of single species population with Allee effect excited by Gaussian noise is studied in this paper.Firstly,the single species population model with Allee effect is established,its stable and unstable states are analyzed.Then Gaussian noise is introduced to describe the stochastic perturbation of the population.Next,the Fokker-Planck equation of the system is approximated.Based on this,the expression of the stationary probability distribution and mean first-passage time are derived.At the same time,our theoretical results are verified by numerical simulation.Finally,we analyzed and discussed the effect of Gaussian colored noise and Allee effect on the stationary probability distribution and mean first-passage time.Our work has drawn some important biological conclusions.The weak Allee effect in the population has a positive effect on the survival and stability of the population;Whether the strong Allee effect or the weak Allee effect occurs in the population,the smaller Allee threshold is more conducive to the survival of the population;When there is a weak Allee effect in the population,the increase in the intensity of multiplicative Gaussian noise will be detrimental to the survival of the population and may even lead to the extinction of the population;Surprisingly,we found the phenomenon of resonant activation in the study.2.The dynamic behaviors of single species population with Allee effect under the coupling between non-Gaussian and Gaussian noises is studied in the paper.Here we used coupling between non-Gaussian and Gaussian colored noises to simulate the stochastic perturbations experienced by the population.According to the research,it can be known that when strong Allee effect happens in the population,the enhanced of the intensity of non-Gaussian noise can cause phase transition,while the population may be extinct.When strong Allee effect occurs in the population,the increase of non-Gaussian noise parameters and coupling strength will promote the transfer of the population from extinction state to survival state.3.The dynamic behaviors of a single species population stochastic model with time delay and Allee effect are studied in this paper.Here,the coupling between non-Gaussian noise and Gaussian white noise are used to characterize the environmental disturbances of the model.We added time delay to the model which makes the study more realistic.In this paper,the effect of time delay on the system is expressed by the delay differential equation using small delay approximation method.Based on the delay differential equation,the expression of stationary probability distribution and mean first-passage time of the system are obtained.The research shows that regardless of the strong Allee effect or weak Allee effect occurs in the population,the increase in the intensity of multiplicative non-Gaussian noise is not conducive to the survival of the population;When strong Allee effect happens in the population,the increase of time delay will inhibit the transition between stable states.These conclusions will provide effective theoretical assistance for the future research of biological systems and the adjustment of ecological balance.