A more chaotic and easily hardware implementable new 3-D chaotic system in comparison with 50 reported systems

Singh, Jay Prakash; Roy, Binoy Krishna

doi:10.1007/s11071-018-4249-3

Cited by 33 publications

(5 citation statements)

References 68 publications

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“…Bifurcation is the main route to chaos from the stable state, and it will cause the system to lose stability. e bifurcation map is used to analyze the dynamic characteristics of the nonlinear system when the system parameter varies [33]. It is known that the system parameter disturbance power amplitude P e must change all the time and the system conditions can change when the system is disturbed by inevitable disturbances.…”

Section: Bifurcation Diagrammentioning

confidence: 99%

Fractional-Order Hyperbolic Tangent Sliding Mode Control for Chaotic Oscillation in Power System

Dao-li

Zhang

Liu

et al. 2021

Mathematical Problems in Engineering

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Chaotic oscillation will occur in power system when there exist periodic load disturbances. In order to analyze the chaotic oscillation characteristics and suppression method, this paper establishes the simplified mathematical model of the interconnected two-machine power system and analyzes the nonlinear dynamic behaviors, such as phase diagram, dissipation, bifurcation map, power spectrum, and Lyapunov exponents. Based on fractional calculus and sliding mode control theory, the fractional-order hyperbolic tangent sliding mode control is proposed to realize the chaotic oscillation control of the power system. Numerical simulation results show that the proposed method can not only suppresses the chaotic oscillation but also reduce the convergence time and suppress the chattering phenomenon and has strong robustness.

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Section: Bifurcation Diagrammentioning

confidence: 99%

Fractional-Order Hyperbolic Tangent Sliding Mode Control for Chaotic Oscillation in Power System

Dao-li

Zhang

Liu

et al. 2021

Mathematical Problems in Engineering

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“…It is important to stress that the study of third order asymmetric chaotic systems has been the material of some recent contributions. On this line, table 1 provides the relative performances of the new jerk system with Triple well polynomial nonlinearity with respect to some recent asymmetric third order models including systems with discrete number of equilibria [16][17][18][19][20][21][22][23][24]33] and those with infinite number of equilibria [25][26][27][28][29][30][31][32] focusing on the type of nonlinearity, the occurrence of antimonotone bifurcations, the number of Andronov-Hopf type bifurcation when changing a control parameter, and the number of coexisting solutions. The key innovations and contributions of the present work could be listed in the following way:…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous multistability and antimonotonicity for a new 3D system with a triple well nonlinearity: theoretical study, control and microcontroller implementation

Ramakrishnan,

Kemgang,

Kengne

et al. 2024

Phys. Scr.

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We propose a new 3D autonomous multistable jerk-like system with a nonlinear term consisting of a six-order triple well function. The presence of six equilibrium points with symmetrical locations along the x-axis represents one of the main distinguishing properties of the new system. Strikingly, the stability analysis of equilibria reveals a cascade of Hopf bifurcations at three specific values of a single control parameter, which results in several forms of complexity. Accordingly, various forms of coexisting attractors such as stable fixed points, limit cycles of diverse periodicities, and chaotic attractors are depicted for some special parameter values. Moreover, It is found that the new jerk-like system with six order triple well polynomial function exhibit extremely complex nonlinear behaviors such as anti-monotone bifurcations, hysteresis and parallel bifurcation branches. These latter aspects explain the presence of multiple (i.e. up to four) coexisting asymmetric attractors for some special rank of parameters. In the presence of multiple competing dynamics, we resort to basins of attraction in order to highlight the how the state space is magnetized. The combination of dynamic features discussed in the new jerk-like system with triple well polynomials nonlinearity introduced in this article is unique and rarely reported. An electronic version of the new system with triple well polynomial nonlinearity is implemented in PSpice. Moreover, a hardware digital implementation of the system is also carried out using an Arduino microcontroller. A very good agreement is captured between PSpice simulation results, the laboratory measurements and the theoretical predictions.

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“…The effect of state feedback on Wang-Chen system was investigated by introducing a further state variable [13]. A relatively more chaotic (based on the first Lyapunov exponent) system [14]. With the great development of econophysics, researchers utilized the chaos theory to study the internal complexity of economic and financial systems [15].…”

Section: Introductionmentioning

confidence: 99%

Analytic solutions of alpha-beta -time- derivatives complex finance chaotic dynamical system: synchronization and extended center manifold. An explicit approach

Abdel-Gawad,

El Mahdy

2024

Phys. Scr.

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The present study focuses on a real finance nonlinear dynamic system (FNLDS), which has been shown to exhibit chaotic behavior. The solutions for such nonlinear dynamical systems (NLDSs) have typically been derived using numerical techniques. The objective of this study aims to; firstly, derive approximate analytical solutions for the complex FNLDS (CFNLDS) by constructing the Picard iterative scheme. The convergence of this scheme is proven, and the error analysis shows good tolerance, indicating the efficiency of the technique. Second a novel criterion for synchronizing the real and imaginary parts of the system is presented, based on a necessary condition. Thirdly, a new method for constructing the extended center manifold is introduced. The 3D portrait reveals a feedback scroll pattern, while the 2D portrait, representing the mutual components, shows multiple pools. The synchronization of the real and imaginary parts of the system is demonstrated graphically. The FNLDS is tested for sensitivity dependence against infinitesimal variations in the initial conditions, and it is found that the system components are moderately sensitive. Furthermore, the Hamiltonian and the extended center manifold establish a two-fold structure. It is observed that the effect of the α−β derivative leads to delay the behavior of the solutions.

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A more chaotic and easily hardware implementable new 3-D chaotic system in comparison with 50 reported systems

Cited by 33 publications

References 68 publications

Fractional-Order Hyperbolic Tangent Sliding Mode Control for Chaotic Oscillation in Power System

Fractional-Order Hyperbolic Tangent Sliding Mode Control for Chaotic Oscillation in Power System

Heterogeneous multistability and antimonotonicity for a new 3D system with a triple well nonlinearity: theoretical study, control and microcontroller implementation

Analytic solutions of alpha-beta -time- derivatives complex finance chaotic dynamical system: synchronization and extended center manifold. An explicit approach

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