Stability, Bifurcation, Chaos : Discrete Prey Predator Model with Step Size
A. George Maria Selvam1, R. Janagaraj2, Mary Jacintha3
1A. George Maria Selvam*, Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Vellore, Tamil Nadu, India.
2R. Janagaraj, Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur,Vellore, Tamil Nadu, India.
3Mary Jacintha, Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur ,Vellore, Tamil Nadu, India.
Manuscript received on October 12, 2019. | Revised Manuscript received on 22 October, 2019. | Manuscript published on November 10, 2019. | PP: 3382-3387 | Volume-9 Issue-1, November 2019. | Retrieval Number: A4866119119/2019©BEIESP | DOI: 10.35940/ijitee.A4866.119119
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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: In this work titled Stability, Bifurcation, Chaos: Discrete prey predator model with step size, by Forward Euler Scheme method the discrete form is obtained. Equilibrium states are calculated and the stability of the equilibrium states and dynamical nature of the model are examined in the closed first quadrant 2 R with the help of variation matrix. It is observed that the system is sensitive to the initial conditions and also to parameter values. The dynamical nature of the model is investigated with the assistance of Lyapunov Exponent, bifurcation diagrams, phase portraits and chaotic behavior of the system is identified. Numerical simulations validate the theoretical observations.
Keywords: Population Dynamics, Discrete Time, Fixed points, Stability, Bifurcation theory, Lyapunov Exponent, Chaos.
Scope of the Article: Foundations Dynamics