The Research Of Predator-prey Models Incorporating Prey Refuges

The effect of prey refuges on predator-prey models is the frontiers and hotspots in theoretical ecology and mathematical ecology. Generally speaking, the temporal dynamics of the predator and prey populations are modeled by the dynamical equations in which two types of prey refuges (the one is a constant proportion of prey using refuges, the other is a constant number of prey using refuges) is incorporated. The effect of refuges used by prey on the equilibrium densities and the stability properties of the equilibrium points of the considered model are analyzed, many important and meaning achievements have been obtained in the past decades. On the one hand, the effect of prey refuges can increase the equilibrium density of prey population, increase and/or decrease that of predators, increase both equilibrium densities of prey and predators under a very restricted set of conditions. On the other hand, the effect of refuges used by prey can increase the stability of the interior equilibrium point of the considered model, that is prey refuges has a stabilizing effect. In this work, increasing of stability refers to cases where the interior equilibrium point changes from being unstable to be locally or globally stable due to the increase of the effect of refuges used by prey population. Prey refuges which protects a constant number of prey have a stronger stabilizing effect on population dynamics than refuges which protects a constant proportion of prey. However, at a comparatively smaller extent, the desta-bilizing effect of prey refuges and discrete-time predator-prey models incorporating prey refuges are investigated. Motivated by these, in this work, we will incorporate the effect of prey refuges in discrete-time predator-prey models besides incorporating it in the continuous ones. Furthermore, make the conclusion that the effect of refuges used by prey has a destabilizing effect become realistic and find the evidences proving it. This PhD thesis includes four chapters. In chapter one, we briefly reviewed the history of the development of population models, introduce two single species models some classic continuous and discrete predator-prey models. In chapter two, the effect of prey refuges and its studies including the examples, the earliest constructed predator-prey model with prey refuges, the types of prey refuges and some important conclusions are proposed. In chapter three, we incorporated the effect of refuges used by prey in seven continuous predator-prey models. The stabilizing effect of prey refuges was validated applying the method of dynamical systems. Most importantly, the destabilizing effect of prey refuges was found, this make the conclusion that the effect of refuges used by prey has a destabilizing effect become true. The relative results can be considered as the evidence for the destabilizing effect of prey refuges. Chapter four mainly focused on the effect of refuges used by prey which influences on the dynamical consequences of discrete-time predator-prey models. The results showed that the dynamical consequences are more complex than that of continuous ones. Generally speaking, the stabilizing effect occur easily when the intrinsic growth rate and the converting efficiency is relatively small. If the the intrinsic growth is relatively larger, the destabilizing and/or bidirectional effects can be found. The bidirectional effect occur under a set of conditions, that is three stable states can be reached in turn: unstable state, locally stable state and unstable state.