Predator-prey Model Based On Individual

Biomathematics is an interdisciplinary subject between mathematics and biology that uses a variety of mathematical thought as its research methods so as to solve the biological problems. It theoretically studies the mathematical methods that are relevant to biology. Undeniably, in many different fields of biology, math tools are strongly needed for the study of biological phenomena. The main research method is to build the mathematical model based on the object of study and both qualitative and quantitative research is carried out to it. The mainly used mathematical methods include:differential equation, probability theory and mathematical statistics, abstract algebra, topology, catastrophe theory and the development of the electronic computer inspired the new breakthroughs in the study of biomathematics.When studying the ecological models, we should respect the individually independent characteristics of different organism, such as the gene, age structure, individual differences, distribution and so forth. However, there exist prodigious limitations on these factors in the applied differential equation methods. The instructive result obtained by applying the latest abstract results into the models with practical significance is one of the features of the modern applied mathematics, especially for the gradual auspiciousness of the individual-based network model along with the development of computer technology. With a lot of advantages such as, simple definition, clear rules, broad research and strong scalability, the network models have got significant attention in the biomathematics domain.The first chapter of this paper will put its emphasis on introducing the fundamentals of ecology. Through the elementary understanding of the existing ecology knowledge, the basic concepts and research progress of ecology will be intuitively grasped and the sally port of research will be found. Referring to six main aspects, namely, the population in ecological system, population regulation, interspecies relation, ecological system, energy flow and material circulation and biological invasion, the theoretical basis is established for the modeling.In the second chapter, two kinds of bio mathematical models will be introduced:the differential equations and the computer simulations. In the differential equation part, the very famous Logistic equation will be firstly introduced and then the operation process and calculation simulation of the Lotka-Volterra equation is realized as well as some kind of Holling models for predator and predator-prey system referred. In the computer simulation part, the author will interpret the Penna model for sexual reproduction, and the research findings of the model studying based on individual characteristics species research methods. At the mean time, the author will explain the operation mechanism of Cellular Automata in detail. At the end, ways and means to simulate complex physical systems and parallel processes will be studied.Taking the improved cellular automata as the foundation, the third chapter of this paper will focus on a variety of prey predator-prey system models. By introducing the parameters of species energy, models can control predators’death and breeding according to how much energy they have and distinguish between different types of preys according to the amount of energies they provide. Considering the diversity in the ways of the predations, especially the difference between herbivores and carnivores, parameters of hunting patterns are introduced. And the evolution processes of different models corresponding to predation relationship are discussed. Finally a conclusion is drawn that the body size is the main factor that influences the survival of prey species because the predators will choose their prey according to different hunting patterns.