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Hopf bifurcations in 3D competitive system with mixing exponential and rational growth rates

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  • Liu, Yujuan
  • Lu, Qiong

Abstract

This paper investigates a three-dimensional mixing competitive system with one exponential growth rate and two rational growth rates, whose nullclines are linearly determined. In total, 33 stable nullcline classes exist. Hopf bifurcations are studied in classes 26-31. We provide examples to prove the existence of at least two limit cycles in each of the classes 27-31.

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  • Liu, Yujuan & Lu, Qiong, 2020. "Hopf bifurcations in 3D competitive system with mixing exponential and rational growth rates," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    • Handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s0096300320301788
    DOI: 10.1016/j.amc.2020.125209
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    References listed on IDEAS

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    1. Khajanchi, Subhas, 2015. "Bifurcation analysis of a delayed mathematical model for tumor growth," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 264-276.
    2. Khajanchi, Subhas, 2017. "Modeling the dynamics of stage-structure predator-prey system with Monod–Haldane type response function," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 122-143.
    3. Khajanchi, Subhas & Banerjee, Sandip, 2017. "Role of constant prey refuge on stage structure predator–prey model with ratio dependent functional response," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 193-198.
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