Dynamics of three unidirectionally coupled autonomous Duffing oscillators and application to inchworm piezoelectric motors: Effects of the coupling coefficient and delay

Tchakui, Murielle Vanessa; Woafo, P.

doi:10.1063/1.4967388

Cited by 20 publications

(5 citation statements)

References 19 publications

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“…More interestingly, by pairing just two Hopfield inertial neurons with heterogeneous activation functions and multi-break points, an increased number of scrolls with complex structures could be obtained. As future work, issues such as chaos control and synchronization [44,45], control of multistability [40], and the impact of time delay coupling [46] for the pair of coupled neurons system introduced here deserves attention in spite of both fundamental and technological importance.…”

Section: Discussionmentioning

confidence: 99%

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Madasamy,

Boui a Boya,

Kengne

et al. 2023

Phys. Scr.

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This work deals with the regular and chaotic dynamics of a system made up of two Hopfield-type neurons with two different activation functions: the hyperbolic tangent function and the Crespi function. The mathematical model is in the form of an autonomous differential system of order four with odd symmetry. The analysis highlights nine equilibrium points and four of these points experience a Hopf bifurcation at the same critical value of a control parameter which can be either the diss1ipation parameter or one of the coupling coefficients. This makes plausible the presence of four parallel bifurcation branches as well as the coexistence of multiple attractors in the behavior of the system. One of the highlights revealed in this work is the coexistence of three double-scroll type attractors of particular topology as well as the presence of a four-spiral attractor. Furthermore, the coexistence of both self-excited and hidden dynamics is also reported. All this plethora of dynamics is elucidated by making use of the usual tools for analyzing nonlinear systems such as bifurcation diagrams, the maximum of Lyapunov exponent, basins of attractions as well as phase portraits. A physical implementation of the microcontroller-based system is envisaged in order to confirm the plethora of behaviors observed theoretically.

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Section: Discussionmentioning

confidence: 99%

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Madasamy,

Boui a Boya,

Kengne

et al. 2023

Phys. Scr.

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“…Nowadays, much more attentions are focused on nonlinear systems useful in the design and modeling of some practical systems, and this in most scientific and technology applications [1,2,3]. To name just a few, Qingjie Cao et al proposed an archetypal system to investigate transitions from smooth to discontinuous dynamics, which in the smooth regime, bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well, while Dupac et al [5] modeled an electromagnetically levitated droplet as a three-dimensional system with lumped masses and elastic springs where its nonlinear behaviour was investigated.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a discontinuous coupled electro-mechanical system oscillator with strong irrational nonlinearities and with two outputs

Adoum¹,

Ramadan²,

Noubissié³

et al. 2021

Global J. Eng. Tech. Adv.

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The dynamics of the nonlinear electromechanical device, consisting of a mechanical part with two outputs and an electrical part which acts as the server is strongly investigated in the present work. The mechanical part consists of two nonlinear oscillators with strong irrational nonlinearities having smooth or discontinuous characteristics, where nonlinearity is just due to the inclination of springs, the geometric configuration, which are both elastically coupled. While the electrical part is the Rayleigh equation. By using the Lagrangian formulation, the model equations are established and used to investigate the equilibrium points and their stabilities. Nest by using the multiple time scales method, the analytical solutions are found both for the case of large amplitude and the weak amplitude, leading to interesting bifurcation sets of the equilibria by varying the control parameters, the inclination angles and driven frequency. Finally, numerical investigations of the exact equation of the system are used to justify the validity of analytical results and to find new phenomena such as chaotic impulses, chaotic bursting and the train of kink signal generations.

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“…Non-resonant piezoelectric actuators can be classified into several types, among which the inchworm actuator and the inertial actuator are two important categories. The inchworm motor is a kind of bionic motor with the advantages of a strong loading capacity and high precision accuracy [22][23][24]. This type of device usually has the limitation of having a complex structure, which is difficult to assemble.…”

Section: Introductionmentioning

confidence: 99%

Design, Analysis, and Experiment on a Novel Stick-Slip Piezoelectric Actuator with a Lever Mechanism

Huang

Sun

2019

Micromachines

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A piezoelectric actuator using a lever mechanism is designed, fabricated, and tested with the aim of accomplishing long-travel precision linear driving based on the stick-slip principle. The proposed actuator mainly consists of a stator, an adjustment mechanism, a preload mechanism, a base, and a linear guide. The stator design, comprising a piezoelectric stack and a lever mechanism with a long hinge used to increase the displacement of the driving foot, is described. A simplified model of the stator is created. Its design parameters are determined by an analytical model and confirmed using the finite element method. In a series of experiments, a laser displacement sensor is employed to measure the displacement responses of the actuator under the application of different driving signals. The experiment results demonstrate that the velocity of the actuator rises from 0.05 mm/s to 1.8 mm/s with the frequency increasing from 30 Hz to 150 Hz and the voltage increasing from 30 V to 150 V. It is shown that the minimum step distance of the actuator is 0.875 μm. The proposed actuator features large stroke, a simple structure, fast response, and high resolution.

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Dynamics of three unidirectionally coupled autonomous Duffing oscillators and application to inchworm piezoelectric motors: Effects of the coupling coefficient and delay

Cited by 20 publications

References 19 publications

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Dynamics of a discontinuous coupled electro-mechanical system oscillator with strong irrational nonlinearities and with two outputs

Design, Analysis, and Experiment on a Novel Stick-Slip Piezoelectric Actuator with a Lever Mechanism

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