Application Research Of Two Types Of Nonlinear Biodynamic Systems

As science and technology develop,the traditional linearization method can not meet our research on complex dynamic systems,and nonlinear dynamics are generated.In recent years,nonlinear biodynamic systems have been widely used in the fields of ecosystem evolution,population genetics,renewable resources development and chemical reaction dynamics.Based on the background of pest management and autocatalytic reaction,two kinds of nonlinear biodynamic models are established and analyzed theoretically.In Chapter 2,considering the species-specific nature of sex pheromones,the use of sex pheromones to attract pests without direct contact with plants and agricultural products,and there is no concern of toxic substance residues.Therefore,sex information is used instead of pesticides for pest management.By incorporating the gestation delay and sex pheromone,we explore the impact of mating disruption control on the dynamic behaviors of pest system.Firstly,the boundness,stability and bifurcation of system are deliberated.Secondly,an optimal control problem based on sex pheromone and pesticide is transformed into an equivalent optimal parameter selection problem by introducing the constrain violation function.Additionally,the gradients of the objective function with respect to the dose of sex pheromone and the killing rate are given.Furthermore,the optimal release amount of sex pheromone and the optimal killing rate of pesticide are calculated through the optimal control theory and numerical simulation.Meanwhile our results indicate that gestation delay increases the extinction risk of the population and liberating sex pheromone destroys the stability of equilibrium states.In Chapter 3,we consider the mixed autocatalytic reaction system with diffusion which describes a series of intricate biochemical reactions.Firstly,stability analyses of constant steady state for both ordinary differential equations and partial differential equations systems are investigated in detail.Our results indicate that the reverse reaction rate of the quadratic autocatalysis play a critical role in dynamics of the reaction.When the appropriate conditions are met,Turing pattern will appear.Additionally,some fundamental properties of nonconstant positive steady states are given.Furthermore,the nonexistence and existence of nonconstant positive steady states are deliberated by some well-known inequalities and the Leray-Schauder degree theory.Finally,numerical simulations are executed to validate the validity of some corresponding analytic results.