Alexander Pimenov, Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany, e-mail: pimenov@wias-berlin.de; Dmitrii Rachinskii, Department of Mathematical Sciences, University of Texas at Dallas, USA, e-mail: Dmitry.Rachinskiy@utdallas.edu
Abstract: Systems of operator-differential equations with hysteresis operators can have unstable equilibrium points with an open basin of attraction. Such equilibria can have homoclinic orbits attached to them, and these orbits are robust. In this paper a population dynamics model with hysteretic response of the prey to variations of the predator is introduced. In this model the prey moves between two patches, and the derivative of the Preisach operator is used to describe the hysteretic flow between the patches. A numerical example of a robust homoclinic loop is presented, and a mechanism creating this homoclinic trajectory is discussed.
Keywords: robust homoclinic; orbit Preisach operator; operator-differential equations; predator-prey model
Classification (MSC 2010): 47J40, 92D25, 37L15
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