Uncertain Destination of a 4D Autonomous System with Five Line Equilibria

R  Wafo Tapche; J  Kengne; Z T  Njitacke; and F B  Pelap

doi:10.17485/ijst/2020/v13i05/145641

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Uncertain Destination of a 4D Autonomous System with Five Line Equilibria

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2020/v13i05/145641

Year: 2020, Volume: 13, Issue: 5, Pages: 519 – 538

Original Article

Uncertain Destination of a 4D Autonomous System with Five Line Equilibria

R. Wafo Tapche^1,2,3,*, J. Kengne¹, Z.T. Njitacke^1,4 and F.B. Pelap³

¹Laboratoire d’Automatique et Informatique Appliquée (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Cameroon
²Unité de Recherche de Matière Condensée, d’Electronique et de Traitement du Signal (LAMACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
³Laboratoire de Mécanique et de Modélisation des Systèmes Physiques (L2MSP), Facultédes Sciences, Universitéde Dschang, BP 69 Dschang, Cameroon
⁴Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon

^*Author for correspondence:
Laboratoire d’Automatique et Informatique Appliquée (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Cameroon.
E-mail ID: wafotapche@gmail.com

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: This paper introduces a novel 4D autonomous dynamic system with five line equilibria and a smooth nonlinearity.

Methods/ statistical analysis: The new model is obtained by adding one more freedom degree to the 3D jerk system recently introduced by Kengne and Mogue, 2018. To analyze and study the model, Ruth criterion principle is used for the stability of different lines equilibria. Using traditional dynamics tools such as bifurcation diagrams, phase portraits, Poincare section, power spectrum, and Pspice software, the dynamic of the system is carried out.

Findings: The new elegant system has an extremely rich dynamics predominated by the phenomenon of extreme multistability. The various sequences of coexisting route to chaos (coexisting bifurcation) confirm the uncertain destination of our novel elegant system. Note that, for the best of author’s knowledge, this is one of the best reproducible extreme multistable system because is not a flux control memristor-based system.

Application/improvements: The results obtained in this investigation enrich the literature and being used to improve the extreme multistability application in many research domains such as Random Number Generation (RNG) and image encryption.

Keywords: Five line equilibria, Extreme multistability, Composite tanh-cubic nonlinearity, PSpice simulations.