Qualitative Analysis Of Single-Population Models And Protection Of Endangered Plants And Animals

In order to investigate the quantitative relationship between population and environment,the population dynamics model becomes a powerful tool to describe population changes.Since many practical problems in nature often occur transient changes that are not controlled by the model itself,such as vaccination of vaccines,regular spraying of pesticides and release of natural enemies to kill pests,and the impact of sudden changes in the ecological environment on the population,the impulsive differential equation becomes a portrayal of this an important means of instantaneous shape.This paper mainly discusses three types of population dynamics models.Firstly,we propose a unilateral diffusion Gompertz model with state-dependent impulsive control strategy.Secondly,we discuss a Lycaon pictus impulsive state feedback control models with Allee effect and continuous time delay.In order to determine the frequency of pulse control,this paper uses the definition of successor function and the geometric theory of differential equations to prove the existence and uniqueness of the system cycle.In order to ensure the robustness of the pulse control,the stability of the periodic solution of the system is proved by the limit method of the successor sequence.Finally,we established a Smith predator-prey system for integrated pest management.In this model,the intensity of biological control and chemical control implementation is linearly dependent on the selected threshold.First,it is proved by subsequent functional methods.The existence and uniqueness of the order-periodic solution.To confirm the feasibility of the biological and chemical control strategies of pest management,the stability of the system is proved by the limit method of the subsequent point sequence and the Poincar'e criterion.The problem is to minimize the total cost.This article has the following five chapters.Chapter 1.the research background and related concepts and applications of impulsive differenti al equations and time-delay differential systems are introduced.Chapter 2,we construct a unilateral diffusion Gompertz model with state-dependent impulsive control strategy.According to compare the slope of the pulse line with the trajectory of the system at the pulse point,and obtain the condition that the successor function is negative,which proves that the system has order-one period solution.Secondly,the uniqueness of the order-one periodic solution is proved by the monotonicity of the successor function,the geometric theory of the differential equation and the definition of the successor function.By comparing the Poincare mapping with the limit cycle theorem analysis of continuous systems,the sufficient conditions for the existence and stability of positive periodic solutions are obtained,and the correctness of the theoretical results is proved by numerical simulation.Chapter 3.in order to protect the endangered species of African wild dogs,we construct a single species model of African wild dogs with Allee effect and continuous time delay.For the state-dependent impulsive differential equations,the existence and uniqueness of the order-one periodic solution of the system are studied by the monotonicity of the successor function and the geometric theory of the differential equation.Then,using the limit method of the successor sequence,the stability condition of the order-one periodic solution of the system is obtained.Finally,the above theory is numerically verified by Maple.We prove the release of artificial captive of African wild dogs can effectively protect the African wild dog population with Allee effect.Chapter 4,in order to protect rare animal and plant species and study the damage of pests to plants,a predator-prey system with linear feedback control is constructed.The control strength is linearly dependent on the selected threshold.Firstly,the successor function method is used to prove that the system has a unique and stable order-one periodic solution.In addition,in order to reduce the total cost,we develop an optimization strategy and obtain the best level of pest control.Finally,the theoretical results is verified by numerical simulation.Chapter 5,we summarize the results of this paper and look forward to the future research direction.