Analysis of processes of competitive survival in ecological systems by the method of imitation modeling

In the paper the behavior of the model Lotka-Volterra, describing the ratio of populations of predator and victim in the elementary link in the food chain by means of numerical experiment was investigated. This model is usually used as the basis of most models of quantitative ecology. We investigated the sensitivity of the model to three-time abrupt change of quantitative parameters of reproduction of the victim and mortality of the predator. Constructed phase portraits demonstrates the changes in system parameters and initial conditions. Parametric analysis of the influence of model parameters on the abundance of populations. It is shown that the main influence on the phase trajectory has not the change of quantitative parameters of the system, but the moment of sudden impact. If the instant abrupt increase of speed of reproduction coincides with the growth stage of victim population, such exposure seems to be pushing the vibrating system in the direction of rocking, while the impulse produced in the opposite phase lead to a decline of the oscillation amplitude. One of the conclusions is that the actual manifestation is impossible to determine at what stage the impact occurred and refers it to the predator or the victim. Another conclusion is that systems, including trophic chains, are prone to multiple stationary states, bifurcations and chaotic jumps from one limit cycle to another. Also, the model of competition of several species for food resources with the logistic function of growth was calculated. It is shown that because of the implementation of the evolutionary principle of “all or nothing” survive only species with the highest value of the parameter ratio of the constants of procreation and destruction.