Studies On Population Interaction In The Presence Of Toxins

In this paper,we focus on population interactions in a noxious environment and harvest or protect the species by the state feedback pulse method.In the first chapter,background on the interaction between toxin environment and population,the current status of research in the country and abroad,and the basic knowledge of semi-continuous dynamical systems and related lemmas are presented.In Sec.2,a prey-predator model of river crabs and water plants is developed to model the growth process of river crabs in a toxic environment.The state-feedback pulse model is used to simulate the whole growth and harvest process of river crabs to implement artificial control strategies to further improve the income of farmers.In Sec.3,a prey-predator model with Holling-Ⅱ functional response function under a toxin environment is established.By harvesting prey and releasing predators,both species can continue to survive.Sufficient conditions for the existence and stability of order-1 periodic solutions of the system are proved.By varying the pulse control strategy,we find the presence of heteroclinic orbits and a bifurcation of the system leading to chaos.In Sec.4,a model of interspecific competition with bilateral control is developed in the context of toxins.The existence and stability of order-1 periodic solutions of the system under one-sided control and two-sided control are proved using the method of successor functions and Poincaré’s theorem,and the advantages of the two-sided control system in the artificially mixed meadow are discussed.The conclusion section summarizes the research on population ecology in this article and provides prospects for future work...