Численное моделирование репликаторных систем специального вида
Background Replicator systems often arise when evolution is concerned. Mathematical models of population dynamics, game theory, economics and biological and molecular evolution lead to the systems of partial differential equations. Due to the absence of analytical solutions for the vast majority of such problems, approximate solutions obtained via numerical simulation are required. Hence, construction of efficient algorithms for the solution of spatial and time-dependent replicator systems is crucial for understanding the dynamics and properties of evolution. Results We give an overview of existing approaches to numerical simulation of replicator systems arising in various fields. We describe a mathematical model of population dynamics with explicit space in game theory setting with asymmetric conflict and a model of biological evolution in presence of a mutator-gene. Both models lead to nonlinear systems of partial differential equations that we cast to the same general form. Then we describe the numerical method based on finite volume framework to solve the system, and provide some numerical examples that demonstrate the method’s validity. Conclusions We conclude that constructed numerical method is suitable for simulation of replicator systems of general form.