4 papers
Mathematical Model of Evolution of Non-Degenerate Replicator Systems
Alexander S. Bratus, Sergey Drozhzhin, Tatiana Yakushkina
We propose and analyse a mathematical model of evolutionary adaptation for non-degenerate (permanent) replicator systems, in which the fitness landscape matrix evolves on a slow ti…
Chapter 2: Geometry of the Fitness Surface and Trajectory Dynamics of Replicator Systems
A. S. Bratus, S. Drozhzhin, T. Yakushkina
We study the geometry of the mean fitness surface of replicator systems and its relationship to evolutionary trajectory dynamics. Using the symmetric--antisymmetric decomposition o…
Mathematical Models of Evolution and Replicator Systems Dynamics. Chapter 1: Introduction to Replicator Systems
A. S. Bratus, S. Drozhzhin, T. Yakushkina
This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formali…
Flow-Based Modelling of Population Dynamics with Consecutive Continuous Mutations
Alexander Bratus, Tatiana Yakushkina, Vladimir Posvyanski
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype de…