Dynamic Stability Of One Kinds Of Predator-prey Population Ecosystems

Nonlinear complex systems abound both in the socio-economic context and in nature,and population ecosystems are a typical example.Aiming at this system,the dynamic behavior of the system can be studied by constructing the dynamic equations of the system by applying the idea of mathematical modeling,and performing stability analysis and numerical simulation of the equations.There are tens of thousands of populations in the ecosystem that are constantly multiplying and evolving.They all interact in a crisscross ecosystem with predation,reciprocity and competition.In order for a population to survive,there must be no shortage of nutrients.The food chain and food web constitute the nutritional relationship between populations.This is the phenomenon of predation among populations.The classic Lotka-Volterra model can simulate this phenomenon,but the model is not perfect.It does not take into account the situation that the prey cannot grow infinitely under limited resources.Therefore,many experts and scholars have improved this model.Added factors such as Allee effect,noise,migration,functional response,etc.that may affect the system.Later,models of more than two populations were also proposed to describe similar ecological phenomena,but in many literatures,a population is often only considered as a predator or as a bait for research,in fact,unless it is at the top of the food chain Will not be predated by other populations,and most of them will be predators and prey.What we are studying is another form of the predator chain model in the three-group predator-predator model,that is,the introduction of a new intermediate species that will both prey in the original model and be preyed by the original predator We combined the Holling-I functional response function and the Logistic population model to write the dynamic equation expression of the model,and in order to facilitate mathematical analysis,we wrote the equation in a dimensionless form.The stability of the ecosystem is also a hot topic for many scholars.Whether the ecosystem is stable will directly affect a series of environmental issues such as ecological habitats and biodiversity,and even cause disasters on the earth,which will bring immeasurable impact on human society.We solve the dimensionless equations and find that the model has five non-negative equilibrium solutions,and use the Routh-Hurwitz criterion to analyze the stability of these five non-negative equilibrium solutions and the durability and extinction of the system Sex.Finally,numerical simulations found that the change of predation rate is of great significance to the predator’s own survival and extinction.At the same time,seasonality may change the dynamic balance of the ecosystem and even affect the survival and extinction of the population,which increases the possibility of extinction of predators.