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Evolutionary game dynamics on networks typically consider the competition among simple strategies such as cooperation and defection in the Prisoner's Dilemma and summarize the effect of population structure as network reciprocity. However,…
Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The…
We introduce and study a mean-field model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the…
We study adaptive dynamics in games where players abandon the population at a given rate, and are replaced by naive players characterized by a prior distribution over the admitted strategies. We demonstrate how such process leads…
When faced with an imminent risk of predation, many animals react to escape consumption. Antipredator strategies are performed by individuals acting as a group to intimidate predators and minimize the damage when attacked. We study the…
Replicator equations (RE) are among the basic tools in mathematical theory of selection and evolution. We develop a method for reducing a wide class of the RE, which in general are systems of differential equations in Banach space to escort…
Fudenberg and Harris' stochastic version of the classical replicator dynamics is considered. The behavior of this diffusion process in the presence of an evolutionarily stable strategy is investigated. Moreover, extinction of dominated…
In this paper, a class of Kolmogorov systems with delays are studied. Sufficient conditions are provided for a system to have a compact uniform attractor. Then Jansen's result (J. Math. Biol. Vol. 25 (1987) 411-422) for autonomous…
In this paper, I model and study the process of natural selection between all possible mixed strategies in classical two-player two-strategy games. I derive and solve an equation that is a natural generalization of the Taylor-Jonker…
Many complex adaptive systems contain a large diversity of specialized components. The specialization at the level of the microscopic degrees of freedom, and diversity at the level of the system as a whole are phenomena that appear during…
The results presented in this paper are a natural development of those described in the paper {\it The Volterra Integrable case. Novel analytical and numerical results} (OCNMP Vol.4 (2024) pp 188-211), where the authors reconsidered the…
For a continuously differentiable Kolmogorov map defined from the nonnegative orthant to itself, a type-K competitive system is defined. Under the assumptions that the system is dissipative and the origin is a repeller, the global dynamics…
We study games in which the set of strategies is multi-dimensional, and new agents might learn various strategic dimensions from different mentors. We introduce a new family of dynamics, the recombinator dynamics, which is characterised by…
Repeated interaction between individuals is the main mechanism for maintaining cooperation in social dilemma situations. Variants of tit-for-tat (repeating the previous action of the opponent) and the win-stay lose-shift strategy are known…
The well-known replicator equation in evolutionary game theory describes how population-level behaviors change over time when individuals make decisions using simple imitation learning rules. In this paper, we study evolutionary dynamics…
A replicator equation with mutation processes is numerically studied. Without any mutations, two characteristics of the replicator dynamics are known: an exponential divergence of the dominance period, and hierarchical orderings of the…
We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three…
Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an…
We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…
Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which…