Publicación: DYNAMICS AND BIFURCATIONS OF A MODIFIED LESLIE-GOWER-TYPE MODEL CONSIDERING A BEDDINGTON- DEANGELIS FUNCTIONAL RESPONSE
Fecha
2019
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MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Resumen
IN THIS PAPER, A PLANAR SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS IS CONSIDERED, WHICH IS A MODIFIED LESLIE-GOWER MODEL, CONSIDERING A BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE. IT GENERATES A COMPLEX DYNAMICS OF THE PREDATOR-PREY INTERACTIONS ACCORDING TO THE ASSOCIATED PARAMETERS. FROM THE SYSTEM OBTAINED, WE CHARACTERIZE ALL THE EQUILIBRIA AND ITS LOCAL BEHAVIOR, AND THE EXISTENCE OF A TRAPPING SET IS PROVED. WE DESCRIBE DIFFERENT TYPES OF BIFURCATIONS (SUCH AS HOPF, BOGDANOV-TAKENS, AND HOMOCLINIC BIFURCATION), AND THE EXISTENCE OF LIMIT CYCLES IS SHOWN. ANALYTIC PROOFS ARE PROVIDED FOR ALL RESULTS. ECOLOGICAL IMPLICATIONS AND A SET OF NUMERICAL SIMULATIONS SUPPORTING THE MATHEMATICAL RESULTS ARE ALSO PRESENTED.
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stability, predator-prey model, limit cycles, Hopf bifurcation, homoclinic bifurcation, Bogdanov-Takens bifurcation, Beddington-DeAngelis functional response
