The Dynamics Behavior of Coupled Generalized van der Pol Oscillator with Distributed Order

Themairi, A. Al; Farghaly, Ahmed Sabry

doi:10.1155/2020/5670652

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…The Lyapunov direct method, used for analysis of stability, was first generalized for nonlinear time-varying DO systems in [ 355 , 356 , 357 ] and was used to determine the stability or asymptotic stability of certain nonlinear systems including a DO analog of the Lorenz system. The theoretical framework proposed in the studies [ 355 , 356 ] was then used to analyze different nonlinear time-varying DO systems including a DO consensus model [ 358 ], the DO Lorenz system [ 359 ], and the DO Van der Pol oscillator [ 330 , 360 ]. The consensus of multi-agent systems with fixed directed graphs and described by DODE, was analyzed in [ 358 ] and sufficient conditions were obtained for robust consensus in the presence and absence of external disturbances.…”

Section: Applications To Control Theorymentioning

confidence: 99%

Applications of Distributed-Order Fractional Operators: A Review

Ding

Patnaik

Sidhardh

et al. 2021

Entropy

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Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of constant and variable-order fractional operators opening significant opportunities to model systems whose behavior stems from the complex interplay and superposition of nonlocal and memory effects occurring over a multitude of scales. In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced. However, a systematic review of the available literature and of the state-of-the-art of DOFC as it pertains, specifically, to real-world applications is still lacking. This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems. The review starts by offering a brief introduction to the mathematics of DOFC, including analytical and numerical methods, and it continues providing an extensive overview of the applications of DOFC to fields like viscoelasticity, transport processes, and control theory that have seen most of the research activity to date.

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Section: Applications To Control Theorymentioning

confidence: 99%

Applications of Distributed-Order Fractional Operators: A Review

Ding

Patnaik

Sidhardh

et al. 2021

Entropy

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Stability Analysis of the Nabla Distributed-Order Nonlinear Systems

2022

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The stability of the nabla discrete distributed-order nonlinear dynamic systems is investigated in this paper. Firstly, a sufficient condition for the asymptotic stability of the nabla discrete distributed-order nonlinear systems is proposed based on Lyapunov direct method. In addition, some properties of the nabla distributed-order operators are derived. Based on these properties, a simpler criterion is provided to determine the stability of such systems. Finally, two examples are given to illustrate the validity of these results.

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Theoretical Study of Forced Van Der Pol Oscillator Equation Using Multiple Two-timing Regular Parameter Perturbation and Asymptotic Expansion Techniques

N.O.

2024

African Journal of Mathematics and Statistics Studies

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This paper presents the theoretical study of forced Van der Pol oscillator equation. Oscillatory systems are studied to know measures that can reduce the amplitude of oscillation of the oscillatory system. Here, multiple two-timing regular parameter perturbation is applied since it is a kind of perturbation among other perturbation techniques that enables the study of the behaviour of a system under certain conditions. Asymptotic expansion technique was also applied. Excel Microsoft was used to analyse the uniformly valid asymptotic solution of the Van der Pol oscillator equation obtained. The uniformly valid asymptotic solution in the independent variable obtained, showed that damping alters the amplitude of the oscillatory system thereby affecting its motion. Increase in damping decreases the amplitude of oscillation of the system. With damping incorporated in the system though very small damping, the amplitude of oscillation reduces with time.

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The Dynamics Behavior of Coupled Generalized van der Pol Oscillator with Distributed Order

Cited by 3 publications

References 28 publications

Applications of Distributed-Order Fractional Operators: A Review

Applications of Distributed-Order Fractional Operators: A Review

Stability Analysis of the Nabla Distributed-Order Nonlinear Systems

Theoretical Study of Forced Van Der Pol Oscillator Equation Using Multiple Two-timing Regular Parameter Perturbation and Asymptotic Expansion Techniques

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