A chaotic map with infinite number of equilibria in a bounded domain

Zhen Wang; Abdul Jalil M. Khalaf; Huaigu Tian; Ahmed Alsaedi; Tasawar Hayat

doi:10.1140/epjst/e2020-900172-0

EPJ

A chaotic map with infinite number of equilibria in a bounded domain

Zhen Wang¹^a, Abdul Jalil M. Khalaf², Huaigu Tian¹, Ahmed Alsaedi³ and Tasawar Hayat³^,4

¹ Shaanxi Engineering Research Center of Controllable Neutron Source, School of Science, Xijing University, Xi’an 710123, P.R. China
² Ministry of Higher Education and Scientific Research, Baghdad, Iraq
³ NAAM Research Group, King Abdulaziz, University of Jeddah, Jeddah, Saudi Arabia
⁴ Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan

Received: 23 August 2019
Received in final form: 19 September 2019
Published online: 26 March 2020

Abstract

Although chaotic flows with special properties in their equilibria have been investigated widely, such an effort about chaotic maps has been neglected. In this note, we introduce a dynamical map with an infinite number of equilibrium points. Such a system doesn’t exist in the literature. A complete dynamical analysis is done on this new map which reveals its rich potential in showing chaos and multi-stability.

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