Mathematical Model for Growth Rates of Competing Organisms for Biological Species with Metamorphoses in Ontogenesis

摘要

The article considers the problem of a mathematical description of the growth rate for biological species with a pronounced staging of the life cycle. The rate of growth of organisms is a characteristic that directly affects the success of the transition to the next ontogenetic stage, and indirectly through the mechanism of intraspecies competition — the survival of the entire new generation. The new model takes into account that rapid ecological and physiological metamorphoses in the development of organisms are reflected in the regulating factors and total number of the adult part of the population. The rate of development fluctuates sufficiently to the point of maturation in many species of insects with a high reproductive potential and migratory fish, and is not reflected by the generalized function w(t) , since it depends on the degree of competition. It is proposed a method for describing the rate of growth with changes as a continuous-discrete computational structure on the basis of differential equations in the Cauchy form with a predicatively redefined structure of the right-hand side. An iterative dynamic system of the population process is obtained, which has the possibility of changing coexisting stable cycles under the influence of external factors. In the case of strengthening competitive factors for natural causes, an inverse tangential bifurcation occurs. An alternative attractor in the form of a cycle with the largest average population value disappears, and the population goes into the regime of long depression.