Dynamics and chaos control in nonlinear electrostatic transducers

Kakmeni, F. M. Moukam; Bowong, Samuel; Tchawoua, Clément; Kaptouom, Ernest

doi:10.1016/j.chaos.2003.12.087

Cited by 14 publications

(3 citation statements)

References 20 publications

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“…However, it will be necessary to impose conditions at ±∞ on the solutions of the second differential equation in the system (8), and these will be dictated by the dynamical phenomena that are specific to system (17). We remark that for the heteroclinic or homoclinic orbit, v(t) increases exponentially as t tends to infinity.…”

Section: Apply the Melnikov Theory To Control Instabilitymentioning

confidence: 97%

“…Although other works [14,[17][18][19][20][21] provide insight into the chaotic behavior of non-linear electromechanical systems, global bifurcations (homoclinic and heteroclinic bifurcation) of our model are important theoretical problems in science and engineering applications as they can reveal the instabilities of motion and complicated dynamical behaviors. These effects, which can damage the electromechanical seismographs, have not been examined by the researches mentioned above accordingly to our knowledge.…”

Section: Introductionmentioning

confidence: 99%

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Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory

et al. 2010

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This paper deals with problems for which it is necessary to represent the oscillations of the electromechanical seismograph about their position of equilibrium as regards the synchronous condition. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of the stable orbit with an unstable one. Then, global bifurcations and chaotic dynamics of an electromechanical seismograph are the aims of this study. The electrical part of the model is described by an extended force Rayleigh M. Siewe Siewe ( ) oscillator with Φ 6 -potential, while the mechanical part is described by a damped and driven linear oscillator. By using the direct perturbation technique, we analytically obtain the general solution of the first-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos in the case where the Φ 6 -potential is three wells, which are complemented by numerical simulations by which we illustrate the bifurcation curves and the fractality of the basins of attraction. The results show that the threshold amplitude of harmonic excitation for the onset of instability will move upwards as the amplitude intensity of the ground motion increases. These results suggest that much attention should be paid to controlling the increase of the amplitude of the ground motion, especially when the harmonic excited electromechanical seismograph system as a main device is applied to some practical systems.

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Section: Apply the Melnikov Theory To Control Instabilitymentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory

et al. 2010

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“…By the Routh-Hurwitz criterion, Rajasekar et al [8] obtain the stability boundary of fixed points of the approximated equations for two coupled Duffing-van der Pol oscillators with a nonlinear coupling. Then Moukam Kakmeni and co-workers [9] analyzed the dynamics and chaos control in nonlinear electrostatic transducers, which are characterized by two coupled nonlinear Duffing system with quadratic coupled terms.…”

Section: Introductionmentioning

confidence: 99%

Resonance and Bifurcation in a Nonlinear Duffing System with Cubic Coupled Terms

2006

Nonlinear Dyn

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The dynamic behaviors of two-degree-of-freedom Duffing system with cubic coupled terms are studied. First, the steady-state responses in principal resonance and internal resonance of the system are analyzed by the multiple scales method. Then, the bifurcation structure is investigated as a function of the strength of the driving force F. In addition to the familiar routes to chaos already encountered in unidimensional Duffing oscillators, this model exhibits symmetry-breaking, period-doubling of both types and a great deal of highly periodic motion and Hopf bifurcation, many of which occur more than once. We explore the chaotic behaviors of our model using three indicators, namely the top Lyapunov exponent, Poincaré cross-section and phase portrait, which are plotted to show the manifestation of coexisting periodic and chaotic attractors.

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Disturbance rejection and performance enhancement of perturbed tri-stable energy harvesters by adaptive finite-time disturbance observer

et al. 2022

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Dynamics and chaos control in nonlinear electrostatic transducers

Cited by 14 publications

References 20 publications

Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory

Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory

Resonance and Bifurcation in a Nonlinear Duffing System with Cubic Coupled Terms

Disturbance rejection and performance enhancement of perturbed tri-stable energy harvesters by adaptive finite-time disturbance observer

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