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Kinetic and Related Models (KRM)
 

Stability of solutions of kinetic equations corresponding to the replicator dynamics

Pages: 109 - 119, Volume 7, Issue 1, March 2014      doi:10.3934/krm.2014.7.109

 
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Mirosław Lachowicz - Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland (email)
Andrea Quartarone - Scienze Matematiche e Informatiche, Universitá di Messina, Dipartimento di Matematica, Viale F. Stagno D’Alcontres, Messina 98166, Italy (email)
Tatiana V. Ryabukha - Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland (email)

Abstract: In the present paper we propose a class of kinetic type equations that describes the replicator dynamics at the mesoscopic level. The equations are highly nonlinear due to the dependence of the transition rates of distribution function. Under suitable assumptions we show the asymptotic (exponential) stability of the solutions to such kinetic equations.

Keywords:  Replicator equation, mesoscopic models, integro--differential equations, stability.
Mathematics Subject Classification:  60J75, 92D25, 35Q92, 35R09, 37N25, 45K05.

Received: January 2013;      Revised: April 2013;      Available Online: December 2013.

 References