We propose a minimal model of the dynamics of diversity-replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the conventional replicator equation and the generalized Lotka-Volterra equation. We reach several significant conclusions as follows: (1) a complex ecosystem can e...

We study the evolution of mixed strategies in population games. At any time, the distribution of mixed strategies over agents in a population is described by a density function. A pair of players is chosen randomly in each round of the game. After each round, players update their mixed strategies using certain reinforcement driven rules. The distribution over mixed strategies thus changes. In a...

The Developmental Systems approach to evolution is defended against the alternative ‘extended replicator’ approach of Sterelny, Smith and Dickison (1996). A precise definition is provided of the spatial and temporal boundaries of the ‘life-cycle’ that DST claims is the unit of evolution. Pacé Sterelny et al., the extended replicator theory is not a bulwark against excessive holism. Everything w...

We investigate the dynamics of two-strategy replicator equations in which competition between strategies is delayed by a given time interval T . Taking T as a bifurcation parameter, we demonstrate the existence of (non-degenerate) Hopf bifurcations in these systems, and present an analysis of the resulting limit cycles using Lindstedt’s method. INTRODUCTION The field of evolutionary dynamics us...

Abstract The paper deals with the numerical solution of problem P to maximize a homogeneous polynomial over unit simplex. We discuss convergence properties so-called replicator dynamics for solving . further examine an ascent method, which also makes use transformation. Numerical experiments polynomials different degrees illustrate theoretical results.

Recently, a novel graph-theoretic notion of a cluster has been proposed, i.e., the “dominant set”, which captures the two basic requirements of a cluster, namely internal coherency and external incoherency. In this paper, we tackle the problem of finding several dominant sets using the replicator dynamics. Specifically, we adopt a game-theoretic perspective to this iterative extraction: Game dy...

Darwinian evolution is based on three fundamental principles, reproduction, mutation and selection, which describe how populations change over time and how new forms evolve out of old ones. There are numerous mathematical descriptions of the resulting evolutionary dynamics. In this paper, we show that apparently very different formulations are part of a single unified framework. At the center o...