Antimonotonicity and chaos in certain nonlinear maps under an  additive constant perturbation

S. Valli Priyatharsini; A. Zeenath Bazeera; M. Mohamed Roshan; S. M. Abdul Kader; Veerapadran Chinnathambi

S. Valli Priyatharsini Sadakathullah Appa College, Tirunelveli 627 011, Tamilnadu, India
A. Zeenath Bazeera Sadakathullah Appa College, Tirunelveli 627 011, Tamilnadu, India
M. Mohamed Roshan Sadakathullah Appa College, Tirunelveli 627 011, Tamilnadu, India.
S. M. Abdul Kader Sadakathullah Appa College, Tirunelveli 627 011, Tamilnadu, India.
Veerapadran Chinnathambi Sadakathullah Appa College, Tirunelveli, Tamil nadu, India

Abstract

The behaviour of antimonotonicity and chaos have been investigated numerically in certain nonlinear maps like Bountis map, Cubic map and Coupled Logistic type Predator-Prey map under constant perturbation. These maps are interest because they appear in different physical contexts. We first examine the behaviours of antimonotonicity and chaos in these maps without perturbation. This paper explores the effect of constant perturbation on these behaviours in these maps. The results of the study show many striking departures from the behaviours of unperturbed maps. In addition to the well known antimonotonicity and chaotic behaviours, suppression of chaos, more than one antimonotonicity behaviour and dominance of reversal period-doubling sequences have been found for the range of parameters values. The main objective of this paper is to explore these behaviours of the chosen maps using two indicators, namely, bifurcation diagram and Lyapunov exponent. Poincare´ maps and phase portraits are plotted to show the manifestation of antimonotonicity, periodic and chaotic behaviours.