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Gasull, A., Kooij, R.E. and Torregrosa, J. (1997) Limit Cycles in the Holling-Tanner Model. Publicacions Matemàtiques, 41, 149-167.
https://doi.org/10.5565/publmat_41197_09

has been cited by the following article:

• TITLE: Hopf Bifurcation for a Predator-Prey System with θ Logistic Growth

  AUTHORS: Suqi Ma, Meisheng Li

  KEYWORDS: Homoclinc Solution, Bogdanov-Takens Bifurcation, Generalized Hopf Bifurcation

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.14 No.4, December 11, 2025

  ABSTRACT: In predator-prey population model, the density capacity restricts the growth rate of prey population. Prey species is assumed with θ logistic growth rate, which is θ exponent dependent. The generalized Hopf point is found, hence the Bautin bifurcation with limit cycle hysteresis phenomena is observed, which brings forth the limit point cycle appearing on Bautin bifurcation line. The homoclinc bifurcation line starts from Bogdanov-Takens point and tangents to saddle-node bifurcation line. The homoclinic orbits and near dynamics are simulated, which manifests the complex dynamics of system.