Dynamics of a prey–predator model with a strong Allee effect and Holling type-III ratio-dependent functional responseDynamics of a prey-predator model…\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ldots $$\end{document}K. Vishwakarma, R. Yadav

This paper investigates two-dimensional Gause-type prey-predator models with a strong Allee effect. By incorporating the Holling type-III ratio-dependent functional response, the model provides a complete view of prey-predator interactions in an ecosystem with different realistic phenomena. In this study, we mainly focus on how to influence the death rate of predators on system dynamics in the presence of a strong Allee effect. Here, the prey growth function is subjected to the strong Allee effect, which measures the correlation between the population size or density with a critical threshold value. In this manuscript, we have investigated the positivity of the solution, boundedness, stability, and sensitivity analysis of the proposed model. Apart from these, all the dynamical behaviours of the system have been captured through a comprehensive analysis of one and two-parameter bifurcation diagrams. In the course next outcomes of the local and global bifurcation analysis, we observed all possible bifurcations, such as the existence of saddle-node bifurcation, Hopf bifurcation, which are the local bifurcations. Moreover, we also observe that the system exhibits global bifurcation such as the Bogdanov–Takens bifurcation and homoclinic bifurcation. Finally, the analytical results are validated with numerical simulations.