| The prey-predator relationship is common among species in ecosystems,and studying the dynamic behavior of prey-predator models can help predict and estimate the quantity of prey and predators.This can then be used to manipulate and regulate ecological mechanisms to maintain system balance.The population is always influenced by a variety of factors such as human activity,time delay,and random environmental interference.In this thesis,we construct three types of prey-predator models to explore the impact of these factors on population dynamics.Firstly,we establish a prey-predator model with two populations that have a double lag time and capture.We prove that the solutions of the model are bounded and nonnegative,and analyze the stability of the equilibrium point of the non-lag model,and the optimal harvesting strategy.By analyzing the roots of the characteristic equation,we investigate the stability changes near coexistence equilibrium under different delay combinations,and the existence of Hopf bifurcations.Finally,we verify the theoretical analysis results through numerical simulations.Secondly,considering the increased presence of harmful substances in the environment,we construct a stochastic population model of two competing prey and one predator with the prey-dependent functional response and Markov switching in a polluted environment.By constructing a suitable Lyapunov function,we prove that the model has a unique global positive solution and a stationary distribution,and using the (?) formula in stochastic differential equations,the stochastic differential equation comparison theorem,etc.to discuss the sufficient conditions for the persistence and extinction of populations in time average.Finally,the theoretical analysis results are verified by numerical simulations.Lastly,considering the intervention behavior of predators in real predation processes,we propose a three-population random food chain model with the predator-dependent functional response and Lévy jumps in a polluted environment.We prove the existence of a unique global positive solution for the model and then investigate the sufficient conditions for population persistence and extinction in time average.We establish the sufficiency of the model to be stable by distribution.Finally,we conduct numerical simulations. |
