Abstract
In this paper, a predator-prey systems of two species is proposed where prey population is subjected to a strong additive Allee effect and predator population consumes the prey according to the ratio-dependent Holling type-II functional response. We use the blow-up technique in order to explore the local structure of orbits in the vicinity of origin. We have determined the conditions for extinction/survival scenarios of species. Some basic dynamical results; the stability; phenomenon of bi-stability and the existence of separatrix curves; Hopf bifurcation; saddle-node bifurcation; homoclinic bifurcation, and Bogdanov-Takens bifurcation of the system are studied. Numerical simulation results that complement the theoretical predictions are presented. A discussion of the consequences of additive Allee effect on the model along with the ecological implications of the analytic and numerical findings is presented.
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Pal, P.J., Saha, T. (2015). Dynamical Complexity of a Ratio-Dependent Predator-Prey Model with Strong Additive Allee Effect. In: Sarkar, S., Basu, U., De, S. (eds) Applied Mathematics. Springer Proceedings in Mathematics & Statistics, vol 146. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2547-8_29
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DOI: https://doi.org/10.1007/978-81-322-2547-8_29
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