Research On Dynamics Behavior Of Some Nonlinear Biological Model

Nonlinear science is a basic science in the studying of common nonlinear phenomenon , which relates with many fields of nature and social sciences。This paper studies the nonlinear dynamics mainly, we specifically discussed some central issue in them, then got some improved and important results.Firstly, we introduces the research background and current status of nonlinear dynamics. In the second chapter, we describe a ratio-dependent predator system with Hassell-Varley function , and consider the dynamic behaviors of system with the effect of the reaction-diffusion. Discussed the conditions of Turing and Hopf branch in space, through a large number of numerical simulations ,we got the spatial pattern of the spot diagram. In the third chapter , an epidemic model with treatment function is discussed in the angle of branch. The fourth and the fifth chapters study the chaotic dynamical behaviors of a food chain model and the nonlinear dynamics with impulse control separately. By studying the boundedness of solutions and existence and stability of the equilibrium, numerical simulations show the chaos in the continuous model. By using the theories of impulsive equations and comparison theorem, mathematical theoretical works have investigated the existence, locally asymptotically stable for the semi-trivial periodic solution. Computer simulations are carried out, using bifurcation diagram , long-term dynamic behavior of nonlinear dynamic systems is studied. Finally the largest Lyapunov exponent is computed, this computation demonstrates the chaotic dynamic behavior of the ecosystem and the accuracy of simulation results.