The Stability Study And Analysis Of Several Kinds Of Impulsive Food Chain System With Mutual Interference And Functional Response

The rapid economic growth has brought great damage to the ecological environment.The report of the 19 th National Congress of the People's Republic of China has promoted the construction of ecological civilization as a millennium plan for sustainable development in China.Research on the stability of ecological system has become increasingly important.This paper mainly studies the qualitative properties of periodic and non-periodic impulse control food chain systems influenced by factors such as mutual interference between predators,prey refuge,and functional responses.It is mainly composed of five chapters.The introduction of this paper mainly introduces the research background,research significance,domestic and foreign research status and the main content of this article.The preliminary knowledge introduces the related theories of impulsive differential equations,coincidence degree theory,the stability and persistence of biological system,as well as some common functional responses.Firstly,taking into account the mutual interference of predators and integrated pest management,an impulsive food chain system with Hassell-Varley functional response and mutual interference is established.Using the Floquet theorem of impulsive equation,small amplitude perturbation technique,comparison theorem,the local and global asymptotic stability of the extinction periodic solution of the prey and top predators is studied,And the permanence of the system is studied by using the comparison theorem and constructing multiple Lyapunov functions.Finally,the dynamic properties of the system are further investigated by numerical simulation.Secondly,in view of the complexity of the actual ecosystem,taking into account the effects of clustering effects,square root function response,prey and refuge,and mutual interference,an impulsive food chain system with square root response,prey refuge,and mutual interference is constructed.Using the correlation theory of impulsive differential equation,biological system theory and comparison theorem,etc,the stability of periodic solution and the persistence of this system are studied.The theoretical results are verified by simulation analysis,and the complexity of the effects such as prey refuge,mutual interference and clustering effects is revealed.Then,based on the complex diversity of ecosystems,a non-periodic pulsed food chain system with Beddington-DeAngelis functional response,prey refuge,and mutual interference is constructed.Using the theory of coincidence degree,Arzela–Ascoli theorem,comparison theorem,and appropriate Lyapunov function,the existence of periodic solutions,the global stability and permanence of the system are studied,and the theoretical results are verified by examples and numerical simulations,which reveal that prey refuge constants,mutual interference coefficient and the change of pulse period lead to complicated and variable phenomena in the dynamical properties.Through the stability research and numerical simulation analysis of the above several food chain systems,these obtained results have enriched the theoretical research results of complex systems and provided some suggestions and feasible strategies for ecological balance and system control.