The Kinetic Behavior Of Some Ecosystems

The dynamic behavior on some ecological systems were studied in this thesis. First, the study background, significance and actuality of the ecological systems and the theory that used in this paper about the ecological systems were fully summarized. Then, the effects of noise on the ecological systems described by the Lotka-Volterra model was systematically and deeply investigated. Some research results are obtained.A predator-prey system with one external forcing described by Lotka-Volterra model was studied. In the deterministic case, a new phenomenon shown on experimental data can not be explained, so we investigated the predator-prey system that was subjected to external forcing. Time evolution, phase diagrams,bifurcation diagram, Poincare map, and largest Lyapunov in-dex spectrogram of the system are plotted by means of numerical simulations. It is found that:(1) The inexplicable phenomenon that was shown on experi-mental data is chaos; (2) As the amplitudes of the periodic signal increases, the predator-prey system goes from periodic oscillation to chaos through a period-doubling sequence.The symmetric two-species competition system subjected to noise described by the classic Lotka-Volterra model was investigated. In the stochastic case, we introduced noise to express the effect from external environment of the system. In order to further understand intrinsic dynamical properties of the system, using the adiabatic approximation and the two-state theory, we dealt with the differential equation of two-species competition system. Here, we take the population densities x-y/2 as the state variable of the system. Dealing with the system in the Fokker-Planck equation frame,and using two-state theory, we obtained the analytic expression of SNR about the state variable x-y/2. The results show that:multiplicative noise and additive noise all can enhance the system's response to external periodic signal, i.e., in this system there was two kinds of stochastic resonance, which was confirmed by the random simulations.