A New No-Equilibrium Chaotic System and Its Topological Horseshoe Chaos

Wang, Chunmei; Hu, Chunhua; Han, Jingwei; Cang, Shijian

doi:10.1155/2016/3142068

Cited by 4 publications

(2 citation statements)

References 28 publications

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“…By calculating equation (3), four equilibrium points can be expressed as shown in table 1. The system contains four complex equilibrium points, which means there is no equilibrium point in physical sense [30]. Hence, the new system has hidden chaotic orbits [13].…”

Section: Equilibrium Point and Symmetrymentioning

confidence: 99%

A new 3D hidden conservative chaotic system with multistability and its circuit implementation

Wang

Tian

et al. 2023

Phys. Scr.

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A novel three-dimensional conservative system without an equilibrium point is constructed by replacing the square term x2+y2 in the Vaidyanathan - Sundarapandian oscillator with a simple absolute value term |x|. The system is analyzed in detail by using time-domain waveform plots, bifurcation plots, Lyapunov exponent spectra, spectral entropy (SE), and C0 complexity. It is found that the system has rich dynamic behaviors: multiple phase trajectories can be tuned by only one parameter and multistability due to initial value sensitivity. The system shows that it can yield eight heterogeneous trajectories coexistent at different initial conditions, including periodic, quasi-periodic, and chaotic states. Additionally, the transient behavior was also observed. Finally, the experimental circuit was implemented, verifying both the physical realizability and the rich dynamic behaviors of the proposed system. With high complexity and sensitivity of parameter and initial condition, the proposed system is useful in image encryption and secure communication.

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Section: Equilibrium Point and Symmetrymentioning

confidence: 99%

A new 3D hidden conservative chaotic system with multistability and its circuit implementation

Wang

Tian

et al. 2023

Phys. Scr.

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“…Due to the attractiveness of this issue, different chaotic systems have been proposed to discover the secret of the strange attractor's presence in nonlinear systems. us, some studies have proposed systems with no equilibria [33][34][35], nonhyperbolic equilibria [36,37], or stable equilibria [38,39]. Some others include the systems with a specific configuration of equilibria such as line [40], curve [41,42], plane [43], or surface [44].…”

Section: Introductionmentioning

confidence: 99%

A New Circumscribed Self‐Excited Spherical Strange Attractor

Ramamoorthy¹,

Jamal

Hussain

et al. 2021

Complexity

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Studying new chaotic flows with specific characteristics has been an open-ended field of exploring nonlinear dynamics. Investigation of chaotic flows is an area of research that has been taken into consideration for many years; thus, it helps in a better understanding of the chaotic systems. In this paper, an original chaotic 3D system, which has not been investigated yet, is presented in spherical coordinates. A unique feature of the proposed system is that its velocity becomes zero for a specific value of the radius variable. Hence, the system’s attractor is expected to be stuck on one side of a plane in spherical coordinates and inside or outside a sphere in the corresponding Cartesian coordinates. It means that the attractor cannot pass through the sphere or even touch it. The introduced system owns two unstable equilibria and a self-excited strange attractor. The 1D and 2D system’s bifurcation diagrams concerning the alteration of two bifurcation parameters are plotted to investigate the system’s dynamical properties. Moreover, the system’s Lyapunov exponents in the corresponding period of bifurcation parameters are calculated. Then, two 2D basins of attraction for two different third dimension values are explored. Based on the basin of attraction, it can be found that the sphere has attraction itself, partially, and some initial conditions are led to the sphere, not to the strange attractor. Ultimately, the connecting curves of the proposed system are explored to find an informative 1D set in addition to the system’s equilibria.

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New fractional modelling and control analysis of the circumscribed self-excited spherical strange attractor

Akgül

Partohaghighi

2022

Chaos, Solitons & Fractals

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A New No-Equilibrium Chaotic System and Its Topological Horseshoe Chaos

Cited by 4 publications

References 28 publications

A new 3D hidden conservative chaotic system with multistability and its circuit implementation

A new 3D hidden conservative chaotic system with multistability and its circuit implementation

A New Circumscribed Self‐Excited Spherical Strange Attractor

New fractional modelling and control analysis of the circumscribed self-excited spherical strange attractor

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