Eur. Phys. J. Special Topics 229, 1257-1263 (2020)
https://doi.org/10.1140/epjst/e2020-900246-1

Regular Article

A novel chaotic system in the spherical coordinates

¹ School of Electrical and Information Engineering, Jiangsu University of Technology, Changzhou 213001, P.R. China
² Department of Electronics, Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), Tonantzintla, Puebla 72840, Mexico
³ Department of Computer Science and Engineering, University of Kurdistan-Hewler, Erbil, Iraq
⁴ Faculty of Electrical and Electronic Engineering, Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong district, Hanoi 100000, Vietnam
⁵ Phenikaa Research and Technology Institute (PRATI), A&A Green Phoenix Group, 167 Hoang Ngan, Hanoi 100000, Vietnam
⁶ Department of Electrical Engineering, Golpayegan University of Technology, Golpayegan, Iran

^a e-mail: abdolmohammadi.hamidreza@gmail.com

Received: 31 October 2019
Received in final form: 14 December 2019
Published online: 26 March 2020

Abstract

Investigating new chaotic flows has been a hot topic for many years. Studying the chaotic attractors of systems with various properties illuminates a lamp to reveal the vague of the generation of chaotic attractors. A new chaotic system in the spherical coordinates is proposed in this paper. The system’s solution is inside a predefined sphere, and its attractor cannot cross the sphere. Investigation of equilibrium points of the system shows that the system has eight equilibria, and all of them are saddle. Bifurcation analysis of the system depicts the period-doubling route to chaos with changing the bifurcation parameter. Also, Lyapunov exponents in the studied interval of the bifurcation parameter are discussed. The basin of attraction of the system is investigated to show the sensitivity of the system to initial conditions.