Zero‐Hopf bifurcation in the Volterra‐Gause system of predator‐prey type |
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| Authors: | Jean‐Marc Ginoux Jaume Llibre |
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| Institution: | 1. Laboratoire LSIS, CNRS, UMR 7296, Université de Toulon, BP 20132, F‐83957 La Garde cedex, France;2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Catalonia, Spain |
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| Abstract: | We prove that the Volterra‐Gause system of predator‐prey type exhibits 2 kinds of zero‐Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero‐Hopf equilibrium, and in the second, 4 periodic solutions bifurcate from another zero‐Hopf equilibrium. This study is done using the averaging theory of second order. |
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| Keywords: | periodic orbits predator‐prey system Volterra‐Gause system zero‐Hopf bifurcation |
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