Evolutionary Equations

Deterministic equations for stochastic spatial evolutionary games

Spatial evolutionary games model individuals playing a game with their neighbors in a spatial domain and describe the time evolution of strategy profile of individuals over space. We derive integro-differential equations as deterministic approximations of strategy revision stochastic processes. These equations generalize the existing ordinary differential equations such as replicator dynamics a...

Quasilinear evolutionary equations and continuous interpolation spaces

In this paper we analyze the abstract parabolic evolutionary equations Dt ðu xÞ þ AðuÞu 1⁄4 f ðuÞ þ hðtÞ; uð0Þ 1⁄4 x; in continuous interpolation spaces allowing a singularity as tk0: Here Dt denotes the timederivative of order aAð0; 2Þ: We first give a treatment of fractional derivatives in the spaces Lðð0;TÞ;XÞ and then consider these derivatives in spaces of continuous functions having (at m...

Numerical methods for evolutionary differential equations

Observation Operators for Evolutionary Integral Equations

We analyze admissibility and exactness of observation operators arising in control theory for Volterra integral equations. We give a necessary and sufficient criterion for an unbounded observation operator to map a solution into L2. We then discuss the Hautus Lemma, giving a partial result and an example where it fails.

Solving equations by hybrid evolutionary computation techniques

Evolutionary computation techniques have mostly been used to solve various optimisation and learning problems. This paper describes a novel application of evolutionary computation techniques to equation solving. Several combinations of evolutionary computation techniques and classical numerical methods are proposed to solve linear and partial differential equations. The hybrid algorithms have b...