NONLINEAR-ANALYSIS OF POPULATION EVOLUTION MODELS

Based on the concept of blown-ups of evolution, introduced by OuYang i n 1995, for nonlinear models, the logistic model and its modification of population evolutions are analyzed analytically and numerically. Pr esents results that imply: (1) There does not exist successive whole e volution of time in both the logistic model and its modifications. (2) The increase or decrease of the population size, caused by unsuccessi ve evolution, is limited. (3) The discontinuity characteristic realize s the philosophy that ''things will develop in the opposite direction when they have reached extremes''. (4) The exponential increase of the population size is a special case, where it is shown that the modifie d logistic model agrees more with the reality than the original model. At the end, it points out that it is necessary to reconsider the meth od of reducing the original model into an algebraic equation by changi ng Delta t to a non-dimensional nonvariable by using difference scheme .