15. Nonlinear analysis of population evolution models

Based on the concept of blown‐ups of evolution, introduced by OuYang in 1995, for nonlinear models, the logistic model and its modification of population evolutions are analyzed analytically and numerically. Presents results that imply: (1) There does not exist successive whole evolution of time in both the logistic model and its modifications. (2) The increase or decrease of the population size, caused by unsuccessive evolution, is limited. (3) The discontinuity characteristic realizes 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 modified logistic model agrees more with the reality than the original model. At the end, it points out that it is necessary to reconsider the method of reducing the original model into an algebraic equation by changing Δt to a non‐dimensional nonvariable by using difference scheme.