Modeling nonlinear evolutionary competing processes on the basis of the Lotka – Volterra modification

Abstract

The models of nonlinear competing processes on the base of the modification of the Lotka – Volterra system: the Richardson arms race model, the Lanchester war or battle model, the predator-prey model are presented and studied in the article. The qualitative analysis and also numerical calculation of evolutionary trajectories of system for various values of parameters is carried out. The comparative analysis of the classical and modified models on the basis of the built graphs of solutions of the system of differential equations is presented as well. Various parameters of the system of differential equations which cover practically all the set of possible beneficial and adverse effect on evolutionary trajectories are considered. Due to the dynamic simulation the values and relations of parameters which lead to the cardinal changes in evolution of the modified models are defined. Thus, the conditions under which it is possible to avoid the growth of arms race, that is, the armed conflict, are received. For the modified predator-prey model the conditions under which the biocenosis restoration is possible even at negative nonlinear terms are written down.