NEIMARK-SACKER BIFURCATION AND CONTROL OF CHAOTIC BEHAVIOR IN A DISCRETE-TIME PLANT-HERBIVORE SYSTEM-Reference-Cited by-同舟云学术

NEIMARK-SACKER BIFURCATION AND CONTROL OF CHAOTIC BEHAVIOR IN A DISCRETE-TIME PLANT-HERBIVORE SYSTEM

Published:2022-09-30 Issue:3 Volume:22 Page:549-562
ISSN:2068-3049
Container-title:Journal of Science and Arts
language:en
Short-container-title:J. Sci. Arts

Author:

GÜMÜŞ ÖZLEM AK¹,SELVAM A. GEORGE MARIA²,JANAGARAJ RAJENDRAN³

Affiliation:

1. Adiyaman University, Faculty of Arts and Sciences, Department of Mathematics, 02040 Adıyaman, Turkey.

2. Sacred Heart College, Department of Mathematics, 635601 Tamil Nadu, India.

3. Karpagam Academy of Higher Education, Faculty of Engineering, Department of Mathematics, 641021 Tamil Nadu, India.

Abstract

In this study, the dynamics of a discrete-time plant-herbivore model obtained using the forward Euler method are discussed. The existence of fixed points is investigated. A topological classification is made to examine the behavior of the positive fixed point where the plant and the herbivore coexist. In addition, the existence conditions and direction of Neimark-Sacker bifurcation of the model are investigated using bifurcation theory. Hybrid control method is applied to control the chaos caused by Neimark-Sacker bifurcation. Examples including time series figures, bifurcation figures, phase portraits and maximum Lyapunov exponent are provided to support our theoretical results.

Publisher

Valahia University of Targoviste - Journal of Science and Arts

Subject

General Earth and Planetary Sciences,General Environmental Science

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