A New Category of Three-Dimensional Chaotic Flows with Identical Eigenvalues

Faghani, Zahra; Nazarimehr, Fahimeh; Jafari, Sajad; Sprott, Julien Clinton

doi:10.1142/s0218127420500261

Cited by 16 publications

(12 citation statements)

References 35 publications

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“…e stability of this equilibrium point cannot be determined under the Shilnikov criteria. So, the stability of this case is investigated numerically by tracking the final state of the system with initial values around the equilibrium point (Faghani et al [53]). e result of this investigation shows that the origin is unstable.…”

Section: E System Modelmentioning

confidence: 99%

A New Chaotic System with Only Nonhyperbolic Equilibrium Points: Dynamics and Its Engineering Application

Zolfaghari-Nejad

Charmi

Hassanpoor³

2022

Complexity

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In this work, we introduce a new non-Shilnikov chaotic system with an infinite number of nonhyperbolic equilibrium points. The proposed system does not have any linear term, and it is worth noting that the new system has one equilibrium point with triple zero eigenvalues at the origin. Also, the novel system has an infinite number of equilibrium points with double zero eigenvalues that are located on the z -axis. Numerical analysis of the system reveals many strong dynamics. The new system exhibits multistability and antimonotonicity. Multistability implies the coexistence of many periodic, limit cycle, and chaotic attractors under different initial values. Also, bifurcation analysis of the system shows interesting phenomena such as periodic window, period-doubling route to chaos, and inverse period-doubling bifurcations. Moreover, the complexity of the system is analyzed by computing spectral entropy. The spectral entropy distribution under different initial values is very scattered and shows that the new system has numerous multiple attractors. Finally, chaos-based encoding/decoding algorithms for secure data transmission are developed by designing a state chain diagram, which indicates the applicability of the new chaotic system.

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Section: E System Modelmentioning

confidence: 99%

A New Chaotic System with Only Nonhyperbolic Equilibrium Points: Dynamics and Its Engineering Application

Zolfaghari-Nejad

Charmi

Hassanpoor³

2022

Complexity

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“…The shortcoming of this method is that it is not applicable to high-dimensional maps since their basins of attraction are difficult to be visualised. If fixed points exist, we can use the sampling method [Dudkowski et al, 2016b;Brzeski & Perlikowski, 2019;Faghani et al, 2020] to determine whether the attractor is hidden or self-excited. This can be done by taking many initial points from the small neighbours of these fixed points randomly.…”

Section: Problem Statementmentioning

confidence: 99%

“…However, by using this method, we cannot distinguish between hidden and self-excited attractors. So, in the present work, a new class of random bifurcation diagram is constructed to display the self-excited attractors by using the sampling method [Dudkowski et al, 2016b;Brzeski & Perlikowski, 2019;Faghani et al, 2020]. The new procedure can be described as follows: (1) To obtain the fixed points of map (11) by solving Eq.…”

Section: No Fixed Point Imentioning

confidence: 99%

Controlling Hidden Dynamics and Multistability of a Class of Two-Dimensional Maps via Linear Augmentation

Zhang

Jiang

Liu

et al. 2021

Int. J. Bifurcation Chaos

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This paper reports the complex dynamics of a class of two-dimensional maps containing hidden attractors via linear augmentation. Firstly, the method of linear augmentation for continuous dynamical systems is generalized to discrete dynamical systems. Then three cases of a class of two-dimensional maps that exhibit hidden dynamics, the maps with no fixed point and the maps with one stable fixed point, are studied. Our numerical simulations show the effectiveness of the linear augmentation method. As the coupling strength of the controller increases or decreases, hidden attractor can be annihilated or altered to be self-excited, and multistability of the map can be controlled to being bistable or monostable.

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“…which can exhibit many features of regular and chaotic motions. The study of chaos (either self-excited or hidden) in jerk systems has attracted significant attention in [8,17,23,42,70,73,74].…”

Section: Hopf Bifurcation Of a Five-parameter Family Of Quadratic Jerk Systemsmentioning

confidence: 99%

Chaotic Dynamics by Some Quadratic Jerk Systems

Liu

Sang

Wang

et al. 2021

Axioms

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This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter a. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored. The self-exited chaotic attractors are found via a supercritical Hopf bifurcation and period-doubling cascades to chaos. The hidden chaotic attractors (related to a subcritical Hopf bifurcation, and with a unique stable equilibrium) are also found via period-doubling cascades to chaos. A circuit implementation is presented for the hidden chaotic attractor. The methods used in this paper will help understand and predict the chaotic dynamics of quadratic jerk systems.

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A New Category of Three-Dimensional Chaotic Flows with Identical Eigenvalues

Cited by 16 publications

References 35 publications

A New Chaotic System with Only Nonhyperbolic Equilibrium Points: Dynamics and Its Engineering Application

A New Chaotic System with Only Nonhyperbolic Equilibrium Points: Dynamics and Its Engineering Application

Controlling Hidden Dynamics and Multistability of a Class of Two-Dimensional Maps via Linear Augmentation

Chaotic Dynamics by Some Quadratic Jerk Systems

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