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On nonlinear dynamics of interacting populations: Coupled kink waves in a system of two populations

Authors:	NK Vitanov IP Jordanov ZI Dimitrova

Institution:	1. Institute of Mechanics, Bulgarian Academy of Sciences, Akad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria;2. “G. Nadjakov” ISSP, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria;1. Department of Civil Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran;2. Department of Civil Engineering, Isfahan University of Technology, Isfahan, Iran;1. Institute of Mechanics, Bulgarian Academy of Sciences, Akad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria;2. Max-Planck-Institute for the Physics of Complex Systems, Noethnitzerstr. 38, 01187 Dresden, Germany;3. “G. Nadjakov” Institute of Solid State Physics, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria;1. Institute of Mechanics, Bulgarian Academy of Sciences, Akad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria;2. Max-Planck-Institute for the Physics of Complex Systems, Noethnitzerstr. 38, 01187 Dresden, Germany;3. “G. Nadjakov” Institute for Solid State Physics, Bulgarian Academy of Science, Blvd. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria

Abstract:	We discuss a nonlinear model of the spatial–time interaction among populations which reproduction and intensity of interaction depend on their spatial density. For the particular case of two populations with constant growth rates and competition coefficients we obtain analytical nonlinear waves of kink kind. The kinks are connected to propagation of the deviations from the stationary densities corresponding to fixed points in the phase space of the population densities. The kinks are coupled, i.e. the changes of the densities of the two populations are synchronous. Coupled kink solutions are obtained also for the general case of variable growth rates and variable coefficients of interactions.

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