Dynamic Behavior And Stability Analysis In Two Kinds Of Multiple Delayed Bio-economic Systems

In recent decades,many research efforts have been put into investigation in population dynamics of ecosystem.Bio-dynamics is the basis for studying the relationship between population and environment as well as inter-specific competition and coexistence among different species.This thesis is divided into four sections.Firstly,the background of the bioeconomic system and its related concepts are introduced,and its applications in practical engineering as well as some related research are also introduced results in recent years.Secondly,a double delayed bioeconomic phytoplankton zooplankton system with commercial harvesting on zooplankton and environmental stochasticity is proposed.Maturation delay for toxin producing phytoplankton and gestation delay for zooplankton are considered.Environmental stochasticity is incorporated into the proposed system in form of Gaussian white noises.Some sufficient conditions are derived to show that the proposed system has a unique global positive solution.In absence of double time delays,stochastic stability and existence of stochastic Hopf bifurcation are studied based on invariant measure theory and singular boundary theory of diffusion process for the proposed system.In presence of double time delays,asymptotic behaviors of the interior equilibrium are discussed by constructing some appropriate Lyapunov functionsThirdly,a discrete hybrid three-species food chain system is proposed,where commercial harvesting on top predator is considered.Two time delays are introduced to represent gestation delay for prey and predator population,respectively.In absence of time delay,sufficient conditions associated with economic interest and step size are derived to show system undergoes flip bifurcation.In presence of double time delays,existence of Neimark-Sacker bifurcation and local stability switch are discussed due to variations of time delays.Furthermore,by utilizing new normal form of delayed discrete hybrid system and center manifold theorem,direction and stability of Neimark-Sacker bifurcation are studied.Numerical simulations are performed not only to validate theoretical analysis,but also exhibit cascades of period-doubling bifurcation,chaotic behavior and stable closed invariant curve.Finally,the whole thesis is summarized and some the unresolved problems in the study are proposed.