Dynamical Behavior of a New Chaotic System with One Stable Equilibrium

Vijayakumar M.D., Anitha Karthikeyan, Jozef Zivcak, Ondrej Krejcar and Hamidreza Namazi
Additional contact information
Vijayakumar M.D.: Centre for Materials Research, Chennai Institute of Technology, Chennai 600069, India
Anitha Karthikeyan: Electronics and Communications Engineering, Prathyusha Engineering College, Thiruvallur 602025, India
Jozef Zivcak: Department of Biomedical Engineering and Measurement, Faculty of Mechanical Engineering, Technical University of Kosice, 040 01 Kosice, Slovakia
Ondrej Krejcar: Department of Biomedical Engineering and Measurement, Faculty of Mechanical Engineering, Technical University of Kosice, 040 01 Kosice, Slovakia
Hamidreza Namazi: Center for Basic and Applied Research, Faculty of Informatics and Management, University of Hradec Kralove, 500 03 Hradec Kralove, Czech Republic

Mathematics, 2021, vol. 9, issue 24, 1-9

Abstract: This paper reports a simple three-dimensional autonomous system with a single stable node equilibrium. The system has a constant controller which adjusts the dynamic of the system. It is revealed that the system exhibits both chaotic and non-chaotic dynamics. Moreover, chaotic or periodic attractors coexist with a single stable equilibrium for some control parameter based on initial conditions. The system dynamics are studied by analyzing bifurcation diagrams, Lyapunov exponents, and basins of attractions. Beyond a fixed-point analysis, a new analysis known as connecting curves is provided. These curves are one-dimensional sets of the points that are more informative than fixed points. These curves are the skeleton of the system, which shows the direction of flow evolution.

Keywords: chaos; stable equilibrium; hidden attractor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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