Zero‐Hopf bifurcation in the Volterra‐Gause system of predator‐prey type | Zendy

Ginoux JeanMarc | Zendy; Llibre Jaume | Zendy

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Zero‐Hopf bifurcation in the Volterra‐Gause system of predator‐prey type

Author(s) -

Ginoux JeanMarc,

Llibre Jaume

Publication year - 2017

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4569

Subject(s) - mathematics , hopf bifurcation , zero (linguistics) , type (biology) , order (exchange) , mathematical analysis , control theory (sociology) , bifurcation , nonlinear system , physics , ecology , control (management) , linguistics , philosophy , finance , quantum mechanics , economics , biology , management

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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