Nonlinear dynamics of two electromechanical arms acting discontinuously on a balloon under the action of a sinusoidal excitation.

Compression systems based electromechanical actuators require a good understanding of their dynamics for a better performance. This paper deals with the study of the nonlinear dynamics of an electromechanical system with two rotating arms subjected to a sinusoidal excitation for fluid compression purposes. The physical model integrating two balloons to be compressed by the arms alternately is presented and the mathematical equations traducing their dynamics are established.

Multistability, relaxation oscillations, and chaos in time-delayed optoelectronic oscillators with direct laser modulation.

We investigate the nonlinear dynamics of an optoelectronic oscillator that is implemented with a laser diode (LD) with time-delayed feedback. In this system, electrical-to-optical conversion is directly implemented using the direct modulation of the laser diode itself, instead of an electrooptical modulator as in conventional architectures. Moreover, we consider the cubic nonlinear saturation of the characteristic laser power-intensity (P-I) transfer function far above threshold, instead of its simplified piecewise linear counterpart.

Abundant chaos in a mixer model with a hysteretic iron core inductance.

Industrial mixers are equipment used in food, drug, chemical and semiconductor industries. Chaotic mixing has been proposed to improve the degree of homogeneity and reduce the energy consumption. This paper deals with dynamical studies of a mixer model with complex rotational movements.

Dispersion of pollutants in a porous medium with finite thickness and variable dispersion coefficients.

Groundwater is subject to the intrusion of pollutants of various types. These pollutants can have natural or anthropogenic sources. Their consumption can therefore affect human health, but also affects the development of vegetation.

Analysis of the dynamics of new models of nonlinear systems with state variable damping and elastic coefficients.

This paper, is an analysis of the dynamics of new models of nonlinear systems in which the state damping variables with elastic coefficients, given by functions , , and are investigated in their autonomous and excited states. They exhibit periodic regions of stability and instability in their autonomous states and a rich dynamic behavior. The analysis of limit cycles shows the presence of isolated curves around the origin (0.

Numerical solution of the Burgers equation associated with the phenomena of longitudinal dispersion depending on time.

In this study, the Burgers equation governing the time-dependent dispersion phenomena is solved numerically using the finite difference scheme and the Runge-Kutta 4 algorithm with appropriate initial and boundary conditions. Two time-dependent dispersion functions have been implemented to analyze the spatio-temporal variation in the domain. For the values of K and K < 1.

Long-range interaction effects on coupled excitable nodes: traveling waves and chimera state.

In this paper, analytical and numerical studies of the influence of the long-range interaction parameter on the excitability threshold in a ring of FitzHugh-Nagumo (FHN) system are investigated. The long-range interaction is introduced to the network to model regulation of the Gap junctions or hemichannels activity at the connexins level, which provides links between pre-synaptic and post-synaptic neurons. Results show that the long-range coupling enhances the range of the threshold parameter.

Corrigendum to "Modeling, simulation and optimization of solid fuel bread ovens commonly used in developing countries" [Heliyon 7(2), (February 2021) Article e06184].

[This corrects the article DOI: 10.1016/j.heliyon.

Modeling, simulation and optimization of solid fuel bread ovens commonly used in developing countries.

In this work, we propose a mathematical model describing thermal behavior and heating process optimization of solid fuel bread ovens. Numerical simulation leads to temperature profiles of the oven. The design and implementation of an operating prototype permits us to obtain, with type K thermocouples, experimental temperature profiles in some points of the oven.

Nonlinear dynamics in an optoelectronic feedback delay oscillator with piecewise linear transfer functions from the laser diode and photodiode.

We investigate the nonlinear dynamics of a recent architecture of an optoelectronic oscillator, where the emitting laser and the receiving diode are connected in a head-to-tail configuration via an optical fiber delay line. The resulting nonlinear transfer function is a piecewise linear profile, and its interplay with the delay leads to many complex behaviors such as relaxation oscillations and deterministic chaos. This system belongs to a recent class of optoelectronic oscillators where the nonlinearity does not originate from the sinusoidal transfer function of an imbalanced interferometer, and, in particular, it is a simple optoelectronic oscillator configuration that is capable of displaying a chaotic behavior.

Study of the effect of the offset phase in time-delay electro-optical systems.

We show that the effect of the offset phase on the dynamics of the time-delay optoelectronic oscillators that is observed experimentally can be explained in terms of switching between the subcritical and supercritical Hopf bifurcations. The domains of the offset phase for which the system functions are determined analytically. We also show that the width of these domains exceptionally depends on the interplay between the three time scales of the system.

A normal form method for the determination of oscillations characteristics near the primary Hopf bifurcation in bandpass optoelectronic oscillators: Theory and experiment.

We propose a framework for the analysis of the integro-differential delay Ikeda equations ruling the dynamics of bandpass optoelectronic oscillators (OEOs). Our framework is based on the normal form reduction of OEOs and helps in the determination of the amplitude and the frequency of the primary Hopf limit-cycles as a function of the time delay and other parameters. The study is carried for both the negative and the positive slopes of the sinusoidal transfer function, and our analytical results are confirmed by the numerical and experimental data.

Suppression of the noise-induced effects in an electrostatic micro-plate using an adaptive back-stepping sliding mode control.

In this work, an adaptive backstepping sliding mode control approach is applied through the piezoelectric layer in order to control and to stabilize an electrostatic micro-plate. The mathematical model of the system by taking into account the small fluctuations in the gap considered as bounded noise is carried out. The accuracy of the proposed modal equation is proven using the method of lines.

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

This work deals with the dynamics of three unidirectionally coupled Duffing oscillators and that of three coupled piezoelectric actuators, considering the special case of inchworm motors. Two configurations of the network are studied: ring configuration and chain configuration. The effects of the coupling coefficient and the time delay are analyzed through different bifurcation diagrams and phase difference variation.

Mixed-mode oscillations in slow-fast delayed optoelectronic systems.

In this article, we investigate the dynamical behavior of breathers in optoelectronic oscillators from the standpoint of mixed-mode oscillations. In the phase space, these breathers are composite oscillations that are damped to the attractive branches of an invariant manifold. Our study shows that the emergence of breather dynamics is linked to the apparition of inflection points in the phase space, and we develop an analytical framework based on the Liénard reduction form in order to provide an analytical insight into this phenomenology.

Analysis of tristable energy harvesting system having fractional order viscoelastic material.

A particular attention is devoted to analyze the dynamics of a strongly nonlinear energy harvester having fractional order viscoelastic flexible material. The strong nonlinearity is obtained from the magnetic interaction between the end free of the flexible material and three equally spaced magnets. Periodic responses are computed using the KrylovBogoliubov averaging method, and the effects of fractional order damping on the output electric energy are analyzed.

Dynamics of coupled simplest chaotic two-component electronic circuits and its potential application to random bit generation.

We numerically investigate the possibility of using a coupling to increase the complexity in simplest chaotic two-component electronic circuits operating at high frequency. We subsequently show that complex behaviors generated in such coupled systems, together with the post-processing are suitable for generating bit-streams which pass all the NIST tests for randomness. The electronic circuit is built up by unidirectionally coupling three two-component (one active and one passive) oscillators in a ring configuration through resistances.

Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography.

In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci.

Electrical dark compacton generator: theory and simulations.

A modified Colpitts oscillator (MCO) associated with a nonlinear transmission line (NLTL) with intersite nonlinearity is introduced as a self-sustained generator of a train of modulated dark signals with compact shape. Equations of state describing the dynamics of the MCO part are derived and the stationary state is obtained. Using the Routh-Hurwitz criterion, the result of a stability analysis indicates the existence of a limit cycle in certain parameter regimes and there the oscillation of the circuit delivers pulselike electrical signals.

The design of a reflectionless arterial prosthesis.

We propose a new technique to characterize a reflectionless arterial prosthesis. The corresponding transmission and reflection coefficients are determined from the geometric and the elastic properties of the arterial wall, and the interaction between the latter and the prosthesis are studied accordingly.

Long-range interaction effects on calcium-wave propagation.

In this paper, numerical simulation of calcium waves in a network of cells coupled together by a paracrine signaling is investigated. The model takes into account the long-range interaction between cells due to the action of extracellular messengers, which provide links between first-neighbor cells, but also on cells located far away from the excited cell. When considering bidirectional coupling, the long-range interaction influences neither the frequency nor the amplitude of oscillations, contrary to one-directional coupling.

Chaotic pulse transmission and spiral formation in a calcium oscillation model.

We study a two-dimensional reaction-diffusion equation for calcium oscillation with a pacemaker region. When the pacemaker entrains the whole system, circular waves are observed as a target pattern. However, if the pace of the pacemaker is too fast, the pulse propagation to the outer region sometimes fails in a chaotic manner.

Spatiotemporal dynamics in a ring of N mutually coupled self-sustained systems.

In this paper, we consider the spatiotemporal dynamics in a ring of N mutually coupled self-sustained oscillators in the regular state. When there are no parameter mismatches, the good coupling parameters leading to full, partial, and no synchronization are derived using the properties of the variational equations of stability. The effects of the spatial dimension of the ring on the stability boundaries of the synchronized states are performed.

Synchronization in a ring of four mutually coupled van der Pol oscillators: theory and experiment.

We investigate different states of synchronization in a ring of four mutually coupled van der Pol oscillators. The stability analysis and numerical simulation are performed to determine the suitable coupling parameters leading to high-quality synchronization. The consequences of parameter mismatch are also highlighted.

Intercellular waves propagation in an array of cells coupled through paracrine signaling: a computer simulation study.

A linear chain of cells is considered in which calcium (Ca2+) fluctuations within a cell are described by a simple minimal model. Cells are coupled together by bidirectional paracrine signaling via calcium oscillations. Two typical zones of propagation are observed: a transition zone and a regular zone.