5 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…
Mathematical Models of Evolution and Replicator Systems Dynamics
A. S. Bratus, S. Drozhzhin, T. Yakushkina
This is an edited English version of the authors' monograph "Mathematical Models of Evolution and Replicator Systems Dynamics", posted on arXiv as a single document to which chapte…
The Kolmogorov forward equation for a distributed model of regime-switching diffusions
Alexander S. Bratus, Olga S. Rozanova
For the regime-switching diffusion process with and without advection term we propose an integro-differential equation describing the densities of states continuously distributed o…
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…
A mathematical framework of consumer-resource dynamics: How to incorporate interactions between interactions in evolutionary process
Alexander S. Bratus, Sergei V. Drozhzhin, Artem S. Novozhilov
A novel mathematical framework is proposed to describe the ecological and evolutionary consequences of consumer--resource interactions. Both the consumer and resource are assumed t…