J. Nonl. Mod. Anal., 2 (2020), pp. 173-185.
Published online: 2021-04
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In this paper, we study a host-parasitoid model with Holling II Functional response, where we focus on a special case: the carrying capacity $K_2$ for parasitoids is equal to a critical value $\frac{r_1}{η}$. It is shown that the model can undergo Bogdanov-Takens bifurcation. The approximate expressions for saddle-node, Homoclinic and Hopf bifurcation curves are calculated. Numerical simulations, including bifurcation diagrams and corresponding phase portraits, are also given to illustrate the theoretical results.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2020.173}, url = {http://global-sci.org/intro/article_detail/jnma/18805.html} }In this paper, we study a host-parasitoid model with Holling II Functional response, where we focus on a special case: the carrying capacity $K_2$ for parasitoids is equal to a critical value $\frac{r_1}{η}$. It is shown that the model can undergo Bogdanov-Takens bifurcation. The approximate expressions for saddle-node, Homoclinic and Hopf bifurcation curves are calculated. Numerical simulations, including bifurcation diagrams and corresponding phase portraits, are also given to illustrate the theoretical results.