Research Article
ASimpleConservativeChaoticOscillatorwithLineof
Equilibria:BifurcationPlot,BasinAnalysis,andMultistability
DhinakaranVeeman ,
1
HayderNatiq ,
2
AhmedM.AliAli ,
3
KarthikeyanRajagopal ,
4
andIqtadarHussain
5
1
Centre for Additive Manufacturing, Chennai Institute of Technology, Chennai, India
2
Information Technology Collage, Imam Ja’afar Al-Sadiq University, Baghdad 10001, Iraq
3
DepartmentofElectronicsTechniques,BabylonTechnicalInstitute,Al-FuratAl-AwsatTechnicalUniversity,Babylon51001,Iraq
4
Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India
5
Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University,
Doha 2713, Qatar
Correspondence should be addressed to Karthikeyan Rajagopal; rkarthiekeyan@gmail.com
Received 4 August 2021; Revised 23 February 2022; Accepted 7 March 2022; Published 26 March 2022
Academic Editor: M. De Aguiar
Copyright © 2022 Dhinakaran Veeman et al. is is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
Here, a novel conservative chaotic oscillator is presented. Various dynamics of the oscillator are examined. Studying the dy-
namical properties of the oscillator reveals its unique behaviors. e oscillator is multistable with symmetric dynamics.
Equilibrium points of the oscillator are investigated. Bifurcations, Lyapunov exponents (LEs), and the Poincare section of the
oscillator’s dynamics are analyzed. Also, the oscillator is investigated from the viewpoint of initial conditions. e study results
show that the oscillator is conservative and has no dissipation. It also has various dynamics, such as equilibrium point and chaos.
e stability analysis of equilibrium points shows there are both stable and unstable fixed points.
1.Introduction
Chaotic dynamics have been an interesting topic for many
years. e chaotic Lorenz oscillator was proposed to model
the atmosphere in 1963 [1]. ere was a hypothesis that the
chaotic attractors are associated with saddle equilibria. So,
many well-known chaotic oscillators contain a saddle
equilibrium [2, 3]. In 2011, Wei proposed a chaotic oscillator
without an equilibrium point [4]. Also, in 2012, Wang and
Chen presented a novel chaotic oscillator with one stable
equilibrium [5]. ese works have shown that a flow can
have chaotic dynamics with any equilibria or without it
[6, 7]. Many studies have discussed chaotic oscillators with
lines of equilibria [8, 9]. Lyapunov exponent is a valuable
measure in the study of chaos, and its calculation has been a
hot topic [10].
Many research studies have been focused on proposing
chaotic flows with various features [11–13]. Multiscroll
dynamics were discussed in [14]. Hyperchaotic oscillators
are attractive because of their complex dynamics [15]. e
hyperchaotic dynamics are efficient in secure communica-
tions so that it is not possible to retrieve hidden messages
[16]. ese oscillators also have two positive LEs and high
sensitivity to initial values [17]. In [18], a hyperchaotic
oscillator with no equilibria was studied. Oscillators with
self-excited and hidden attractors were discussed in [19, 20].
In [21], hidden dynamics in a piecewise linear oscillator were
studied. Synchronization and control of chaotic flows have
attracted much attention [22]. Multistability is a significant
feature of dynamical systems [23]. e final circumstance of
a multistable oscillator is determined by initial conditions in
a constant set of parameters [24]. In case of undesirable
multistability, the final state can be controlled by selecting
the proper parameters to transform to monostability [25].
e multistability of a piecewise linear oscillator with var-
ious types of attractors was investigated in [26]. A
Hindawi
Complexity
Volume 2022, Article ID 9345036, 7 pages
https://doi.org/10.1155/2022/9345036