LLV Model Based On Penna Model

In recent years, it is established that the mean-field (MF) approaches have limits in some researches of dynamical system. Non-MF behavior is manifested due to the presence of a support including chemical reactions on catalytic surfaces, ecology, and bacterial growth. While lattice Lotka-Volterra model (LLV) can make relevant rules according to the issue's own characteristics, especially local characteristics and it shows more flexibility than MF method. The original Lotka-Volterra was introduced in dynamical system to describe the competition between species. LLV model derives from Lotka-Volterra model, shows good characteristics in both low dimensions and higher dimensions. For example, stationary patterns and fractality. Penna is a single-species evolvement model;it is a model that is widely researched with computer simulation. It helps to understand some evolvement processes of species, especially in dynamical system. For instance, studying the growth of cod fish simulation of wolf in Alaska, relationship between death age and relatives, evolvement. of species, evolvement process of competition, reproduce and natural selection of haploid, and one-species cellular automata model based on the Penna model was founded on a lattice of two dimensions.Firstly, biomathematics is simple indicated in first part;In the second part, I introduce the LV model and LLV model and then give an example of application;In the third part, Penna model is introduced and the achievements about Penna model are also shown;In the forth part, connect asexual Penna model and LLV model, take the system which contains wolf, sheep, grass, as the research object, join the macroscopically preying rules and microcosmic individual information together, give the "age-preying probability" and then gain the "age, experience and preying probability", found a ecosystem evolvement model which based on Monte Carlo method. Then, give out the result of simulations, change the range of lattice and initial value (random select, strip shaipe, droplet shape), following the rules, simulate the development of the species, get the snapshots and time-number figures, then compare and summarize. At last in the forth part, we summarize our results and put forward some problems which deserve researching.