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March 2014, 7(1): 109-119. doi: 10.3934/krm.2014.7.109
Stability of solutions of kinetic equations corresponding to the replicator dynamics
Mirosław Lachowicz 1, , Andrea Quartarone 2, and Tatiana V. Ryabukha 1,
Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland, Poland
Scienze Matematiche e Informatiche, Universitá di Messina, Dipartimento di Matematica, Viale F. Stagno D'Alcontres, Messina 98166, Italy
Received January 2013 Revised April 2013 Published December 2013
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: stability., integro--differential equations, Replicator equation, mesoscopic models.
Mathematics Subject Classification: 60J75, 92D25, 35Q92, 35R09, 37N25, 45K0.
Citation: Mirosław Lachowicz, Andrea Quartarone, Tatiana V. Ryabukha. Stability of solutions of kinetic equations corresponding to the replicator dynamics. Kinetic & Related Models, 2014, 7 (1) : 109-119. doi: 10.3934/krm.2014.7.109
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Mirosław Lachowicz Andrea Quartarone Tatiana V. Ryabukha