Catastrophe Analyses Parameter Estimate And System Analyses On A Population Model Of Prey Intimidated By Predator

The research of population's dynamic model is an important part in population ecology, which study at the quantity trends, space trends, structure trends of the population and etc. Under various kinds of situations, the population varies with time under the external effect factors. Catastrophe phenomenon often takes place under the influence of different factors. Catastrophe theory is to describe the phenomenon of discontinuity change which takes place under the continuous controlling variables in the system. There are advantages to apply the catastrophe theory to the research of population's dynamic model. This research sets up one population dynamic model under population's dynamic law to analysis the reasons why the population mutation. Parameter estimate lays particular emphasis on individual population parameter of model in the past. Its common purpose aims at seeking one method to optimize parameter in the equation. Its steps are to solve the differential equation at first, then utilize other methods to confirm the parameter in the expression formula. In fact, we might not know the concrete expression formula of the quantity of each population when we analysis the ecological model. So long as know the parameters in the model, we can study the dynamic characteristic and reciprocity of the population. This study provides one method of parameter estimate of the model. This study also aims at equalization point and stability of equalization point analysis of prey with predator system. From these sides, we get results as following: 1. By rationally hypothesis that we has got one population model of prey which is intimidated by predator. In the past, we study the single population dynamic models more at inherent characteristics of the population, for instance the intrinsic increasing rate, capacity of population. Based on these characters, this study gives the prey population one protection hypothesis that is if the prey population under certain number there are no predator in the prey surroundings. This hypothesis makes the prey population avoiding dieing out. 2. Under the situation that when the increasing number of prey equality the eating number of predator, we get one cusp catastrophe model. In the past, when we study the population dynamic catastrophe model, we usually we usually first study the law of population's occurring then apply catastrophe theory to explain it. This study bases on the theory model then deduces one population dynamic catastrophe model. Because the parameters of model have the idiographic biological meaning, it measures the practical thing better and avoids the conversion of parameters. 3. Provide one method of parameter estimate of the model. That is grey method. Parameter estimate is a part of model study, in this paper we give one method to the prey model which intimidated by predator and prove it is effect by one example. 4. We get the conditions of the equilibrium point's existence and stability of the following system.