Existence and Control of Hidden Oscillations in a Memristive Autonomous Duffing Oscillator

Varshney, Vaibhav; Thamilmaran, K.; Shrimali, Manish Dev; Prasad, Awadhesh

doi:10.1007/978-3-319-71243-7_14

Cited by 7 publications

(4 citation statements)

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“…An attractor is called a hidden attractor if its basin of attraction does not intersect any neighborhood of equilibria; otherwise, it is called a self-excited attractor, for more details see [26,27]. Recently in [33,34,19] it was reported the existence of an infinite number of hidden attractors in a memristor-based autonomous Duffing oscillators, whose memristance function is a cubic polynomial. Here, by using a similar approach to the followed in the previous section, we will show that such hidden attractors are not possible, so that the numerical simulations included in [33,34,19] are misleading.…”

Section: False Hidden Attractors In Memristor-based Autonomous Duffin...mentioning

confidence: 99%

“…Recently in [33,34,19] it was reported the existence of an infinite number of hidden attractors in a memristor-based autonomous Duffing oscillators, whose memristance function is a cubic polynomial. Here, by using a similar approach to the followed in the previous section, we will show that such hidden attractors are not possible, so that the numerical simulations included in [33,34,19] are misleading.…”

Section: False Hidden Attractors In Memristor-based Autonomous Duffin...mentioning

confidence: 99%

“…Regarding [33,34,19] authors consider system (40) with the function φ(x) = ωx + βx 3 and the set of parameters α = 0.0001, ω = 0.35, β = 0.85. In both quoted references, authors reported the existence of an infinite number of stable periodic orbits coexisting with an infinite number of stable equilibria, by taking into account several numerical simulations, so concluding the existence of hidden attractors.…”

Section: False Hidden Attractors In Memristor-based Autonomous Duffin...mentioning

confidence: 99%

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Bifurcation set for a disregarded Bogdanov-Takens unfolding: Application to 3D cubic memristor oscillators

2021

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We derive the bifurcation set for a not previously considered threeparametric Bogdanov-Takens unfolding, showing that it is possible express its vector field as two different perturbed cubic Hamiltonians. By using several firstorder Melnikov functions, we obtain for the first time analytical approximations for the bifurcation curves corresponding to homoclinic and heteroclinic connections, which along with the curves associated to local bifurcations organize the parametric regions with different structures of periodic orbits.As an application of these results, we study a family of 3D memristor oscillators, for which the characteristic function of the memristor is a cubic polynomial. We show that these systems have an infinity number of invariant manifolds, and by adding one parameter that stratifies the 3D dynamics of the family, it is shown that the dynamics in each stratum is topologically equivalent to a representant of the above unfolding. Also, based upon the bifurcation set obtained, we show the existence of closed surfaces in the 3D state space which are foliated by periodic orbits. Finally, we clarify some misconceptions that arise from the numerical simulations of these systems, emphasizing the important role played by the existence of invariant manifolds.

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Section: False Hidden Attractors In Memristor-based Autonomous Duffin...mentioning

confidence: 99%

Section: False Hidden Attractors In Memristor-based Autonomous Duffin...mentioning

confidence: 99%

Section: False Hidden Attractors In Memristor-based Autonomous Duffin...mentioning

confidence: 99%

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Bifurcation set for a disregarded Bogdanov-Takens unfolding: Application to 3D cubic memristor oscillators

2021

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“…Interestingly, the solution of Duffing oscillator, in case of non-conservative system, involves intricacies that led to several methods for the situation when damping coefficient is large [10,12]. Among the various perturbative methods, the homotopy perturbation method (HPM) has been extensively used, in general, for finding analytical solution of nonlinear oscillators [2,5,6,7,8,9,12,19]. In this work, we revisited the HPM to investigate in detail the complexity of dynamics of duffing system in the presence of large damping coefficient.…”

Section: Introductionmentioning

confidence: 99%

Modified Homotopy Perturbation Method Based Solution of Linearly Damped Duffing Oscillator and Comparison With Simulated Solution*

K. Chaudhary,

Narang,

Das

2023

jnanabha

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The Dung oscillator provides a basis for studying nonlinear dynamics as its phase space trajectory is fairly complex and depends on the parameter of the system viz., initial amplitude, phase, frequency, linear damping coefficient and non-linearity parameter. In order to understand the complexity of the system, three variable effective expansions have been introduced in the usual homotopy perturbation framework to obtain the solution of damped Dung system which nds application in several areas in engineering sciences such as vibration of bars, plates and electronic circuits, etc. The necessity of the extended homotopy frame work has been further discussed for non-conservative system. Simulation results for different parameters of the systems, such as, linear damping coefficient (μ), amplitude (α) and nonlinearity parameter (ε) are compared with the corresponding results based on perturbative homotopy analysis up to third order by changing (i) the magnitude of linear damping coefficient (μ), (ii) the magnitude of the nonlinearity of the system (ε). Even though the simulated result matches satisfactorily with the perturbative solution over the entire evolutionary time scale, noticeable divergence and phase shift are observed only lately for increased value μ and ε, respectively.

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