The Researches On Permanence Of Predation Systems And The Impact Of Prey Refuge On Their Dynamics

The researches of predation systems (including in the food-chain system with three populations) can be recognized as a major issue in Ecology. The permanence of predation systems and the impact of prey refuges on their dynamics are of the most importance. On the one hand, from the view of biological meaning, the number of each population is larger than 0, it does not mean the predator-prey system will be permanent in the future time. In other words, when the number of prey population and predator population maintain a certain positive number, then the interaction between predator and prey population will be continuous, i.e. the predator-prey system will be permanent. On the other hand, prey refuge is a natural phenomenon in the world. In order to escape from predation and pursuit, prey population must build the refuge to decrease in the predation efficiency. The effect of prey refuge can be understood as constituted by two components: (1) The reduction of prey mortality due to reduction in predation success; (2) The reduction in prey's birth rate due to the sub-optimal states of resources and conditions in the refuge.In our paper, we have comprehensively discussed the permanence of predator-prey systems and the impact of prey refuges on their dynamics and obtain the following main results:1. By studying the non-autonomous predator-prey system with stage structure and food-chain system with three populations, we find that: if we can evaluate some parameters which represent the population characteristics, only through regulating the controlling parameter, the systems will be permanent, that is to say, the predation systems can coexistent in the long term. Our results have leading functions in reserving the extinct populations and sustaining the diversity of ecological systems.2. By studying the impact of prey refuge on the Kolmogorov type predator-prey system and predator-prey system with stage structure, we obtain the following results: (1) Equilibrium density of prey increases as the refuge use by prey increases. Under certain conditions, the equilibrium density of predators increases with the refuge use by prey population, too. (2) The refuge use by prey population can increase the stability of community equilibrium in the first quadrant. In our paper, stabilization or increase of stability refers to cases where a community equilibrium point can change from the unstable fixed point to the locally asymptotically stable equilibrium due to increase in the value of the effect of prey refuge. Thus the positive equilibrium of the system can reach the two states: the unstable equilibrium and the locally asymptotically stable equilibrium...