Computational Modeling of the Nonlinear Metabolism Rate as a Trigger Mechanism of Extreme Dynamics of Invasion Processes

Abstract

Abstract Formalization in the form of systems of differential equations to describe sharp changes in the development of invasion processes remains an important and urgent problem for mathematical biophysics and bioinformatics. The spread of aggressive biological organisms is accompanied by the rapid phenomena of explosive increase in the dynamics of the population of these dangerous foreign species. Hardly predictable population outbreaks of small insects may continue until the total destruction of forests on large areas. This phenomenon of imbalance affects the entire environment and biochemical processes in the trophic chain of the biosystem. After a rapid uncontrolled (by natural physical factors and a biotic environment) outbreak, degradation of ecosystems and extinction of the invasive species may occur. The fundamental problem of controlling new aggressive species is very important for practical problems of the optimal use of bioresources. The generality of some situations requires special mathematical analysis, which can be constructed by analogy with physical processes with sharp transient regimes. Parametric changes and bifurcations cannot explain the change in behavior, because these reproductive characteristics of aggressive species in a specific biophysical environment are stable during evolutionary adaptation and change only gradually. The simulation of changes in the development rate of individuals in a competitive environment is considered as a hidden factor affecting the realization of critical effects in the dynamics of the population of species with a pronounced staging of ontogenesis. A hybrid model is constructed based on the system of equations describing actual changes in the metabolism rate in ontogenesis, which is applicable to populations in different states of the invasion process.

Topics & Concepts