Based On The Si Model Predator And Prey The Establishment Of Micro-mechanism Model And Analysis

To some models of the nonlinear differential equation,it is difficult to solve with mathematical method .However ,by means of the computer running the model defined by the program ,we can study and forecast the system more feasibly .It provides the sole experimentative measure to research complex system . What we study is a kind of prey-predator model with epidemic spreading in it based on agents' interactions. We establish an model of agent –based interaction in aspect of micromechanism,putting the agents into the finite space which we study and dividing the space as the style of square.We suppose that every lattice can only be occupied by one of the same population .The model is formulated as continuous time Markov chains.We set up parameters corresponding to those of macromechanism. To carry through simulation ,we manage Java language and the software of Repast to devise to create the agent-based simulative model ,and we make use of the Fourier commutation to dispose and analyse the pictures .We also work over the issue with the theory of phase transition to discover the physical mechanism of it. The feature of oscillation can ofen be observed .Our model make up for the defect of the model of Lotka and Volterra ,which occurs the behavior of oscillation relying on the initial state .We can not only assure the state of the phase at certain value of parameters but also acquire its critical value .Further more , we can know the evolving current and its state in detail . In the stable state of our model ,it occurs five phases –three kind of active phases and two kind of absorbing phases corresponding to the five kind of equilibrium in the macromechanism. In the simulation the stable state can transfer into another one when taking some stated value ,experiencing the transition from general percolation to the directed percolation .It is the fluctuation in the micromechanicsm lead to the transition of the phase .The fluctuation is unregular and will appear a distinct peak. The trend of the evolution possess the comparability answering for the condition of the stable state in the defined range of the parameters when DI/lamda and DP/TSP change in proportion at medium multiple.The state of this analogue parallels the equilibrium in the macromechanism with the same of its type of the evolution but of discrepant stable value. It will go through all the states in some range ,come forth the critical state and transform from the general percolation to the directed percolation ,coinciding with the defined section of the parameters without change the value of other parameters .It can possibly show two critical and twice of the transition of the phase . We also find two species can coexist only when taking the medium values in some range of parameter,if it is too large or too small only one population can exist or none of them can .Out of its range the state will keep the style of the transition in the critical.When the amplitude is too large ,it will be easy to arrive at the maximum or the zero so that transform to another state.