A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis

Khalaf, Abdul Jalil M.; Kapitaniak, Tomasz; Rajagopal, Karthikeyan; Alsaedi, Ahmed; Hayat, Tasawar; Pham, Viet–Thanh

doi:10.1515/phys-2018-0037

Cited by 6 publications

(3 citation statements)

References 49 publications

(50 reference statements)

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“…Hence, a time discretization method is designed in this paper. In a time interval t i (initial time) to t f (final time), the interval is divided into (t n , t n + 1 ) and the value of x(n + 1) at time t n + 1 is got by applying x(n) at time t n using the relation x(n + 1) = F(x(n)) [34], [37].…”

Section: Fpga Implementation Of the Fwo Systemmentioning

confidence: 99%

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Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

Karthikeyan¹,

Duraisamy²,

Nazarimehr³

et al. 2019

RADIOENGINEERING

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In this paper a modified third order Wien bridge oscillator with fractional order memristor is proposed. Various dynamical properties of the proposed oscillator are investigated such as equilibrium points, Eigenvalues, Lyapunov exponents and bifurcation diagrams. The Lyapunov spectrum of the system for various values of fractional order is derived. Using forward and backward continuation methods of plotting bifurcation diagram, the multistability of the oscillator is investigated. The proposed oscillator is realized using Field Programmable Gate Arrays and the experiment is conducted using hardwaresoftware co-simulation.

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Section: Fpga Implementation Of the Fwo Systemmentioning

confidence: 99%

“…Contradictorily in some cases it is advantageous. It is very important to investigate the chaotic systems for such a phenomenon [34][35][36]. By transforming the parallel resistor and capacitor (RC) feedback network to a series RC feedback network a simple third-order Wien-bridge oscillator has been developed in [37].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

Karthikeyan¹,

Duraisamy²,

Nazarimehr³

et al. 2019

RADIOENGINEERING

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“…Subsequently, scholars found some chaotic systems, [14][15][16] and their equilibria are stable. Even many chaotic systems with only one stable equilibrium were proposed, 17,18 these systems with only stable equilibria coexist with the chaotic attractor. In 2012, Wang and Chen added a tiny perturbation to the Sprott E system 9 to get a new system 19 :…”

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confidence: 99%

New insights into a chaotic system with only a Lyapunov stable equilibrium

Chen

Liu

Wei

et al. 2020

Math Methods in App Sciences

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This paper gives some new insights into a chaotic system. The considered system has only one Lyapunov stable equilibrium and positive Lyapunov exponent in some certain parameter range, which means there coexists chaotic attractors and Lyapunov stable equibirium in system. First, from the perspective of analyzing the global structure of the system, based on the Poincaré compactification technique, the complete description of its dynamical behavior on the sphere at infinity is presented. The obtaining results show that its global dynamical behavior is very complex. Second, from a geometric perspective, the Jacobi stability of the system is investigated, including the unique equilibrium and a periodic orbit. Interestingly, we find that the unique Lyapunov stable equilibrium is always Jacobi unstable, a Lyapunov stable periodic orbit falls into both Jacobi stable and Jacobi unstable regions. It is shown that we might witness chaotic behavior of the system before the trajectories enter a neighborhood of the equilibrium point. It is hoped that the investigation of this paper can contribute to better understand and study the complex chaotic system with stable equilibria.

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Jacobi Stability of Simple Chaotic Systems with One Lyapunov Stable Equilibrium

Chen

Liu

et al. 2021

Journal of Computational and Nonlinear Dynamics

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This paper presents Jacobi stability analysis of 23 simple chaotic systems with only one Lyapunov stable equilibrium by Kosambi–Cartan–Chern theory, and analyzes the chaotic behavior of these systems from the geometric viewpoint. Different from Lyapunov stability, the unique equilibrium for each system is always Jacobi unstable. Moreover, the dynamical behaviors of deviation vector near equilibrium are discussed to reveal the onset of chaos for these 23 systems and show geometrically the coexistence of unique Lyapunov stable equilibrium and chaotic attractor for each system. The obtaining results show that these chaotic systems are not robust to small perturbations of the equilibrium, indicating that the systems are extremely sensitive to the internal environment. This reveals that the chaotic flows generated by these systems may be related to Jacobi instability of the equilibrium.

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A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis

Cited by 6 publications

References 49 publications

Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

New insights into a chaotic system with only a Lyapunov stable equilibrium

Jacobi Stability of Simple Chaotic Systems with One Lyapunov Stable Equilibrium

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