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Controlling Chaos—Forced van der Pol Equation [PDF]
Mathematics, 2017 Nonlinear systems are typically linearized to permit linear feedback control design, but, in some systems, the nonlinearities are so strong that their performance is called chaotic, and linear control designs can be rendered ineffective.
Matthew Cooper +2 more
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Van der Pol Equation with a Large Feedback Delay
Mathematics, 2023 The well-known Van der Pol equation with delayed feedback is considered. It is assumed that the delay factor is large enough. In the study of the dynamics, the critical cases in the problem of the stability of the zero equilibrium state are identified ...
Sergey Kashchenko
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Chaotic and dynamic vibration analysis of a time-delayed nonlinear mathieu oscillator via non-perturbative approach [PDF]
Scientific ReportsThe study compares van der Pol and Rayleigh oscillators with time-delayed effects, providing insights into stability, bifurcations, and organization in nonlinear systems.
Galal M. Moatimid +2 more
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VAN DER POL-DUFFING OSCILLATOR WITH THE EFFECT OF HEREDITARY [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2017 The paper presents a new mathematical model of the van der Pol oscillator, Duffing with external periodic influence given hereditarity. An algorithm for finding the numerical solution of the original model equation, which is based on the finite ...
Novikovа E. R.
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Beni-Suef University Journal of Basic and Applied SciencesBackground Numerical methods are used to solve differential equations, but few are effective for nonlinear ordinary differential equations (ODEs) of order higher than one.
Abdelrady Okasha Elnady +2 more
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Van der Pol model in two-delay differential equation representation
Scientific Reports, 2022 The Van der Pol equation is the mathematical model of a second-order ordinary differential equation with cubic nonlinearity. Several studies have been adding time delay to the Van der Pol model. In this paper, the differential equation of the Van der Pol
M. A. Elfouly, M. A. Sohaly
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Finding the closed-form solutions of dissipative oscillatory systems
Scientific Reports, 2022 This paper shows how to use the approximate Hamiltonian approach for the non-conservative system not capable of possessing Hamiltonian. Using the approximate Hamiltonian method for a non-conservative system is not possible in general. We propose a way to
Saba Irum, Imran Naeem
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On periodic solutions of Rayleigh equation [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021 New sufficient conditions for the existence and uniqueness of a periodic solution of a system of differential equations equivalent to the Rayleigh equation are obtained.
Tlyachev, V. B. +2 more
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About Analytical Approximate Solutions of the Van der Pol Equation in the Complex Domain
Fractal and Fractional, 2023 In the article, the existence of solutions for the Van der Pol differential equation is proved, and the approximate structure of such solutions in the analyticity domain is obtained.
Victor Orlov, Alexander Chichurin
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Weakly nonlinear oscillations of gas column driven by self-sustained sources [PDF]
MATEC Web of Conferences, 2019 Self-sustained sources coupled to some sort of resonator have drawn attention recently as a subject of nonlinear dynamics with many practical applications as well as interesting mathematical problems from the chaos theory and the theory of ...
Hruška Viktor +2 more
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