Eur. Phys. J. Special Topics 229, 1175-1188 (2020)
https://doi.org/10.1140/epjst/e2020-900225-9

Regular Article

Extreme multi-stability analysis of a novel 5D chaotic system with hidden attractors, line equilibrium, permutation entropy and its secure communication scheme

¹ Ministry of Higher Education and Scientific Research, Baghdad, Iraq
² Department of Electrical Engineering, Golpayegan University of Technology, Golpayegan, Iran
³ Department of Biomedical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15875-4413, Iran
⁴ Laboratory of Nonlinear Systems – Circuits & Complexity (LaNSCom) Physics, Department, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
⁵ Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar

^a e-mail: volos@physics.auth.gr

Received: 11 October 2019
Received in final form: 2 November 2019
Published online: 26 March 2020

Abstract

In this paper a new 5D chaotic system with line equilibrium is designed and described to reveal its extreme multi-stability. Hence, all of the resulting attractors are hidden. The suggested system owns many complex dynamic behaviors in comparison with other chaotic systems. System initial state-associated complex dynamical behaviors are considered and we discover that it possesses an immeasurable number of coexisting attractors, which expresses the occurrence of extreme multi-stability. Besides, we also demonstrate the line equilibrium stability in detail, bifurcation diagrams, Lyapunov exponents, and basins of attraction. Also, in order to analyze the new 5D chaotic system we have considered the permutation entropy technique. Finally, the application of the novel 5D chaotic system with line equilibrium to the problem of chaos synchronization and secure communication through observer design is presented.