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. It is obtained that the harvested energy is enhanced for small order of the fractional derivative. Considering the order and strength of the fractional viscoelastic property as control parameter, the complexity of the system response is investigated through the Melnikov criteria for horseshoes chaos, which allows us to derive the mathematical expression of the boundary between intra-well motion and bifurcations appearance domain. We observe that the order and strength of the fractional viscoelastic property can be effectively used to control chaos in the system. The results are confirmed by the smooth and fractal shape of the basin of attraction as the order of derivative decreases. The bifurcation diagrams and the corresponding Lyapunov exponents are plotted to get insight into the nonlinear response of the system.

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. The complexity is generated by an inductance with hysteretic characteristics. Mathematical methods and numerical simulations are used to display the different dynamical states which are period-nT, pulse, bursting and chaotic signals. Good agreement is found between the mathematical and numerical results. In general, it is found that chaos is highly abundant in the model.

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 c cos ⁡ ( p x ) , c sin ⁡ ( p x ) , c cos ⁡ ( p x ˙ ) and c sin ⁡ ( p x ˙ ) 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 (0.0), which explains the presence of periodic solutions (limit cycles). The dynamics obtained allows to describe qualitatively the cardiac activity (artificial pacemaker). A chaos analysis shows the appearance of regular and chaotic behaviors. These studies allowed us to show the effect of the damping of the state variable and the elastic coefficients on the dynamics of these models. The presence of analog functions makes the experimental study complex. An implementation based on microcontroller simulation technology has been proposed. The microcontroller results are consistent with the numerical results.

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.2021.e06184.].

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. There is a good agreement between the experimental results and those obtained from the numerical simulation of the proposed model. A permanent temperature value of 220 °C is reached in the baking chamber. It is obtained that the energy efficiency of the oven is 49%. Making use of the objective gain function, it is found that the optimal parameters of the oven are the following: 50 W as optimum operating value of the electric power of the blower, 3 m2 as the optimum operating value of the total surface of the baking chamber; and 0.67 as the optimum operating value of the filling factor between the heating chamber and the baking chamber. The developed model serves to better understand the operation, the optimization and to rationally manage energy expenditure related to solid fuel bread ovens in developing countries.

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. We find that spiral waves are spontaneously created at the interface between the pacemaker region and the outer region.

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. The long-range interaction influences the speed of propagation of Ca2+ waves in the network and induces enlargement of the transition zone before the steady regime of propagation is attained. We also investigate the long-range effects on the colonization of a given niche by a pathogenic microorganism signal on calcium wave propagation in the network.

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. By using both approaches, the effects of noise are presented. It is found that they lead to pull-in instability as well as to random chaos. A suitable backstepping approach to improve the tracking performance is integrated to the adaptive sliding mode control in order to eliminate chattering phenomena and reinforce the robustness of the system in presence of uncertainties and external random disturbances. It is proved that all the variables of the closed-loop system are bounded and the system can follow the given reference signals as close as possible. Numerical simulations are provided to show the effectiveness of proposed controller.

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. Experimental realization is then used to show the existence of complete and partial synchronization.

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. The transition zone exhibits the same phenomena that can be observed in single cells, pairs or triplets of cells. Within the regular zone, simple periodic oscillations of calcium propagate and the Ca2+ signal is similar from one cell to another (same amplitude and same frequency). But, the signals are separated by a slight phase shift characterizing the propagation of Ca2+ waves due to the type of coupling used. We also consider the colonization of the lattice by the abnormal oscillations of sick cells.

Dynamics of solitary blood waves in arteries with prostheses.

We analyze the behavior of blood waves interacting with a prosthesis following the Yomosa nonlinear wave theory extended to include the spatial variation of the arterial radius and wall rigidity. When the prosthesis is short or when its characteristics are close to those of the host artery, the amplitude of the blood solitary wave increases just proximal to the prosthesis and then decreases to a magnitude smaller than the normal value in a healthy vessel. In the presence of an extended prosthesis, we derive the reflection and transmission coefficients at the interfaces, and we thereby obtain the optimal characteristics for an ideal prosthesis. Our results agree qualitatively with known experimental and numerical studies.

Stability and optimal parameters for continuous feedback chaos control.

We investigate the conditions under which an optimal continuous feedback control can be achieved. Chaotic oscillations in the single-well Duffing model, with either a positive or a negative nonlinear stiffness term, are tuned to their related Ritz approximation. The Floquet theory enables the stability analysis of the control. Critical values of the feedback control coefficient fulfilling the optimization criteria are derived. The influence of the chosen target orbit, of the feedback coefficient, and of the onset time of control on its duration is discussed. The analytic approach is confirmed by numerical simulations.

Synchronized states in a ring of mutually coupled self-sustained electrical oscillators.

We investigate in this paper different states of synchronization in a ring of mutually coupled self-sustained electrical oscillators. The good coupling parameters leading to complete and partial synchronization or disordered states are calculated using the properties of the variational equations of stability. A stability map showing domains of synchronization to an external excitation locally injected in the ring is also obtained. In both cases, the numerical simulation validates and complements the results of the analytical investigation.

Generalized correlated states in a ring of coupled nonlinear oscillators with a local injection.

In this paper, we study the spatiotemporal dynamics of a ring of diffusely coupled nonlinear oscillators. Floquet theory is used to investigate the various dynamical states of the ring, as well as the Hopf bifurcations between them. A local injection scheme is applied to synchronize the ring with an external master oscillator. The shift-invariance symmetry is thereby broken, leading to the emergence of generalized correlated states. The transition boundaries from these correlated states to spatiotemporal chaos and complete synchronization are also derived. Numerical simulations are performed to support the analytic approach.

Optimization and stability boundaries for the synchronization of semiconductor lasers with external optical feedback.

We perform a stability and optimization analysis for the synchronization of unidirectionally coupled external-cavity semiconductor lasers. Using rigorous stability criteria, we qualitatively derive the boundaries of the high-quality synchronization basin. The underlying influence of Hopf bifurcations on the stability of the synchronization manifold is also investigated.

Transitions from spatiotemporal chaos to cluster and complete synchronization states in a shift-invariant set of coupled nonlinear oscillators.

We study the spatiotemporal dynamics of a ring of diffusely coupled single-well Duffing oscillators. The transitions from spatiotemporal chaos to cluster and complete synchronization states are particularly investigated, as well as the Hopf bifurcations to instability. It is found that the underlying mechanism of these transitions relies on the motion of the representative points corresponding to the system's nondegenerated spatial transverse Fourier modes in the parametric Strutt diagram. A scaling law is used to demonstrate that the compact interval of the scalar coupling parameter values leading to cluster synchronization broadens in a square-power-like fashion as the number of oscillators is increased. The analytical approach is confirmed by numerical simulations.

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. Numerical simulations validate and complement the results of analytical investigations. The influences of coupling parameter mismatch on the forecasted stability boundaries are also highlighted.