On the Numerical Approximation and Simulation of Damped and Undamped Duffing Oscillators

Kwari, Lydia J.; Sunday, J.; Ndam, J. N.; James, Adewale

doi:10.5455/sf.87627

Cited by 3 publications

(2 citation statements)

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“…Using the boundary locus method, the stability polynomial for the proposed BHA is For more details on boundary locus method, see [27][28]. The region of absolute stability of the BHA is shown in Figure 1.…”

Section: Region Of Absolutementioning

confidence: 99%

An Accuracy-preserving Block Hybrid Algorithm for the Integration of Second-order Physical Systems with Oscillatory Solutions

Sunday

Ndam

Kwari

2023

J. Nig. Soc. Phys. Sci.

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It is a known fact that in most cases, to integrate an oscillatory problem, higher order A-stable methods are often needed. This is because such problems are characterized by stiffness, chaos and damping, thus making them tedious to solve. However, in this research, an accuracy-preserving relatively lower order Block Hybrid Algorithm (BHA) is proposed for solution of second-order physical systems with oscillatory solutions. The sixth order algorithm was derived using interpolation and collocation of power series within a single step interval [tn; tn+1]. In order to circumvent the Dahlquist-barrier and also obtain an accuracy-preserving algorithm, four o-step points were incorporated within the single step interval. A number of special cases of oscillatory problems were solved using the proposed method and the results obtained clearly showed that it outperformed other existing methods we compared our results with even though the BHA is of lower order relative to such methods. Some of the second-order physical systems considered were the Kepler, Bessel and damped problems. Some important properties of the BHA were also analyzed and the results of the analysis showed that it is consistent, zero-stable and convergent

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Section: Region Of Absolutementioning

confidence: 99%

An Accuracy-preserving Block Hybrid Algorithm for the Integration of Second-order Physical Systems with Oscillatory Solutions

Sunday

Ndam

Kwari

2023

J. Nig. Soc. Phys. Sci.

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“…The effect of different forms of periodic forces in some linear and nonlinear systems has attracted attention. Recent studies have shown that the effect of periodic forces on nonlinear systems is significant and they can alter the dynamical behaviors drastically (see [40][41][42] and references therein). The study of such periodic forces or modulation may help to select the appropriate parameters of the external drive to generate and control nonlinear behaviors in some nonlinear systems such as the Duffing oscillator.…”

Section: Introductionmentioning

confidence: 99%

Modulation effects on the dynamics of a ring of three Duffing oscillators coupled unidirectionally with time-dependent damping

Hernández-Cedillo,

Gallegos,

Urenda-Cázares

et al. 2024

Preprint

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We study the dynamics of a ring of three unidirectionally coupled modulated double-well Duffing oscillators for three different values of the damping coefficient: fixed damping, proportional to time, and inversely proportional to time. The dynamics in all cases are analyzed through time series, Fourier transforms, Poincaré sections, as well as bifurcation diagrams and Lyapunov exponents with respect to the coupling strength and modulation parameters (amplitude Γ and frequency θ). In the first case, we observe how a well-known route from a stable steady state to hyperchaos through Hopf bifurcation and a series of torus bifurcations change when modulation parameters (amplitude and frequency) and the coupling strength are increased. In the second case, the system is highly dissipative and converges into one of the small limit cycles generated from the attraction basins. Finally, transient toroidal hyperchaos coexists with quasi-periodic states in the third case.

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On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems

et al. 2022

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On the Numerical Approximation and Simulation of Damped and Undamped Duffing Oscillators

Cited by 3 publications

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An Accuracy-preserving Block Hybrid Algorithm for the Integration of Second-order Physical Systems with Oscillatory Solutions

An Accuracy-preserving Block Hybrid Algorithm for the Integration of Second-order Physical Systems with Oscillatory Solutions

Modulation effects on the dynamics of a ring of three Duffing oscillators coupled unidirectionally with time-dependent damping

On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems

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