Volodymyr G. Skobelev, Volodymyr V. Skobelev
Qualitative analysis of two destroying each other reproducing populations dynamics
In this paper, a parametric linear continuous-time model that describes the dynamics of a conflict between two populations is constructed. It is assumed that individuals of each population destroy individuals of the other population at given rates, and individuals of each population can be reproduced at given rates with new individuals immediately entering into conflict. The paper contains a qualitative (i.e., mathematical) analysis of the proposed model. The relevance of this problem is due to the fact that, in essence, the entire class of similar problems is considered from a single point of view. Besides, the obtained results outline some strong base for developing algorithms (and, consequently, software) for automatic analysis of systems in this class.
Keywords: System Dynamics, Linear continuous-time models, Lanchester models, Ordinary differential equations, Qualitative analysis
DOI: https://doi.org/10.54381/icp.2026.1.06
Qualitative analysis of two destroying each other reproducing populations dynamics
In this paper, a parametric linear continuous-time model that describes the dynamics of a conflict between two populations is constructed. It is assumed that individuals of each population destroy individuals of the other population at given rates, and individuals of each population can be reproduced at given rates with new individuals immediately entering into conflict. The paper contains a qualitative (i.e., mathematical) analysis of the proposed model. The relevance of this problem is due to the fact that, in essence, the entire class of similar problems is considered from a single point of view. Besides, the obtained results outline some strong base for developing algorithms (and, consequently, software) for automatic analysis of systems in this class.
Keywords: System Dynamics, Linear continuous-time models, Lanchester models, Ordinary differential equations, Qualitative analysis
DOI: https://doi.org/10.54381/icp.2026.1.06