On the Dynamical Behaviour of Three Species Food Chain Model with Time Delay
Y. Suresh Kumar1, N. Seshagiri Rao2, B. V. Appa Rao3

1Y. Suresh Kumar, Research Scholar, Department of Education Foundation, Vaddeswaram , Guntur (Andhra Pradesh), India.
2N. Seshagiri Rao, Department of Applied Mathematics, School of Applied Natural Science, Adama Science and Technology University, Post Box No. 1888, Adama, Ethiopia.
3B. V. Appa Rao, Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur (Andhra Pradesh), India.

Manuscript received on 01 May 2019 | Revised Manuscript received on 15 May 2019 | Manuscript published on 30 May 2019 | PP: 2066-2076 | Volume-8 Issue-7, May 2019 | Retrieval Number: G5231058719/19©BEIESP
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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: A three species model in an ecosystem involving a mutualist interaction among two species and a predator is considered across an autonomous system of intrigro-ordinary delay differential equations. Due to the gestation of the predator, the delay term is proposed to the predator functional response in the model equations. The delay length is estimated how far the stability of the interior equilibrium continues to hold, if the interior equilibrium point is asymptotically stable with no delay term is under consideration. Further the local and global stabilities are discussed by perturbed method and a suitable Lyapunov technique. Also observed the increasing delay can cause a bifurcation of the stable equilibrium into periodic solutions. Finally, the numerical solutions are compared with theoretical results of the model at the end.
Keyword: Delay, Equilibrium Points, Local and Global Stability, Lyapunov Technique, Mutual Species, Numerical simulations, Predator.
Scope of the Article: Cryptography and Applied Mathematics.