Mutualisim between Two Species and a Mortal Predator with Holling Type-II Response Function
Y. Suresh Kumar1, N. Seshagiri Rao2, B. V. Appa Rao3
1Y. Suresh Kumar, Research Scholar, Koneru Lakshmaiah Education Foundation, Vaddeswaram , Guntur, Andhra Pradesh -522502, India.
2N. Seshagiri Rao, Department of Applied Mathematics, School of Applied Natural Science, Adama Science and Technology University, Post Box No. 1888, Adama,
3B. V. Appa Rao, Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, Andhra Pradesh -522502, India.
Manuscript received on 05 March 2019 | Revised Manuscript received on 10 March 2019 | Manuscript published on 30 July 2019 | PP: 4070-4086 | Volume-8 Issue-2, July 2019 | Retrieval Number: B3657078219/19©BEIESP | DOI: 10.35940/ijrte.B3657.078219
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: We analyze the dynamics of a general model of three-species mutualistic interaction among two species and a mortal predator, which consumes the first mutual species in terms of Holling type-II functional response manner. Local stability around the existing equilibrium points is investigated by using perturbed method. Sufficient conditions for the global stability are obtained by means of employing Lyapunov’s method around boundary equilibrium points. The population stochasticity around the steady state of co-existence due to white noise is also computed. Finally, the numerical illustrations are carried out to support the study.
Index Terms: Holling Type- II Function, Local and Global Stability, Mutual Interaction, Numerical Simulations, Predator, Stochastic Analysis.
Scope of the Article: Numerical Modelling of Structures