Stability and Bifurcation: Discrete Differential Algebraic Planar Model with Square Root Response
A. George Maria Selvam1, R. Janagaraj2, Ozlem AK Gumus3

1George Maria Selvam A, Department of Mathematics, Sacred Heart College Autonomous, Tirupattur (Tamil Nadu), India.
2Janagaraj R, Department of Mathematics, Sacred Heart College Autonomous, Tirupattur (Tamil Nadu), India.
3Ozlem AK Gumus, Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, Adiyaman Turkey.
Manuscript received on 20 January 2020 | Revised Manuscript received on 02 February 2020 | Manuscript Published on 05 February 2020 | PP: 290-298 | Volume-8 Issue-4S5 December 2019 | Retrieval Number: D10601284S519/2019©BEIESP | DOI: 10.35940/ijrte.D1060.1284S519
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Abstract: The stability and existence of bifurcation analysis for a two spices discrete time model by introducing square root functional response and step size is examined in this work. Forward Euler scheme method is applied to formulate the discrete model from the continuous model, particularly to explore the rich dynamical behavior of the proposed model. Because the model has square root response function, trivial and axial equilibrium positions are singular. In order to discuss the stability of the trivial and axial equilibrium positions, a transformation is applied. Moreover, we explore the stability of the interior equilibrium position in a discrete two spices model using jury conditions. The numerical experiments are performed for distinct parameter values and also time series and phase line diagrams are presented. We also apply bifurcation theory to find whether the model of spices undergoes periodic doubling bifurcation at its axial and interior equilibrium positions. Numerical examples are provided and they exhibit rich dynamics in both species, including, period – 2, 4, 8 & 16 orbits, periodic windows and Non periodic orbit(chaos).
Keywords: Discrete Time, Equilibrium Positions, Stability, Periodic – Doubling Bifurcations.
Scope of the Article: Cryptography and Applied Mathematics