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Mathematical Study of Two-Patches of Predator-Prey System with Unidirectional Migration of Prey

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Book cover Structural Nonlinear Dynamics and Diagnosis

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 168))

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Abstract

In this chapter we consider a model describing the dynamics of predator-prey populations living in two patches. The two patches follow the Lotka-Volterra type and are coupled through prey migration. Our purpose is to study the effect of migration rate on the behavior of the coupled systems. We prove the positivity of solutions and find the upper and lower bounds with respect to the migration rate of prey. Also, we show the stability /instability of the possible steady states and we establish the global stability of the positive steady state by giving a candidate lyapunov function. Some numerical simulations are provided to graphically demonstrate the population dynamics of the system.

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Author information

Authors and Affiliations

  1. Polydisciplinary Faculty of Ouarzazate, Ibn Zohr University, B.P: 638, Ouarzazate, Morocco

    Radouane Yafia

  2. Normandie Univ, Caen, France

    M. A. Aziz Alaoui

  3. ULH, LMAH, 76600, Le Havre, France

    M. A. Aziz Alaoui

  4. FR CNRS 3335, ISCN, 25 rue Philippe Lebon, 76600, Le Havre, France

    M. A. Aziz Alaoui

Authors
  1. Radouane Yafia
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  2. M. A. Aziz Alaoui
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Corresponding author

Correspondence to Radouane Yafia .

Editor information

Editors and Affiliations

  1. Laboratory of Mechanics, Hassan II-Casablanca University, Casablanca, Morocco

    Mohamed Belhaq

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Yafia, R., Aziz Alaoui, M.A. (2015). Mathematical Study of Two-Patches of Predator-Prey System with Unidirectional Migration of Prey. In: Belhaq, M. (eds) Structural Nonlinear Dynamics and Diagnosis. Springer Proceedings in Physics, vol 168. Springer, Cham. https://doi.org/10.1007/978-3-319-19851-4_21

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