Abstract
In this paper, we have modified Leslie-Gower prey-predator model with strong Allee effect on prey and non-monotonic rational functional response. We have demonstrated the existence of axial equilibria and its stability. Extinction of the all species is possible in our considered model as extinction equilibrium point is always stable. Our considered model exhibited atmost two coexistence equilibria. We have provided the stability properties of interior equilibrium points with the help of graphical Jacobian method. Our proposed model reported bi-stability behavior between trivial and coexistence equilibrium points, and trivial equilibrium point is the global attractor under some parameter choice. We have reported a comprehensive study of the global dynamics of our proposed model. In the course of bifurcation analysis, we have provided the co-dimension two bifurcation diagram by considering Allee as a bifurcation parameter. On co-dimension two bifurcation plane, our proposed model reported rich dynamics in small parametric range. We have reported all possible local and global bifurcations, namely saddle-node bifurcation, Hopf bifurcation, Bogdanov-Takens bifurcation and Homoclinic bifurcation, respectively. Numerical examples are performed to validate the analytical findings.
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Acknowledgements
Udai Kumar’s research is supported by research fellowship from MHRD, Government of India. Partha Sarathi Mandal’s research is supported by SERB, DST project [grant: YSS/2015/001548].
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Kumar, U., Sarathi Mandal, P. (2021). Dynamics of a Class of Modified Leslie-Gower Predator-Prey Model with Strong Allee Effect on Prey and Non-monotonic Rational Functional Response. In: Das, B., Patgiri, R., Bandyopadhyay, S., Balas, V.E. (eds) Modeling, Simulation and Optimization. Smart Innovation, Systems and Technologies, vol 206. Springer, Singapore. https://doi.org/10.1007/978-981-15-9829-6_41
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