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The fluctuation of ions concentration across the cell membrane of neuron can generate a time varying electromagnetic field. Thus, memristors are used to realize the coupling between the magnetic flux and the membrane potential across the membrane. Such coupling results from the phenomenon of electromagnetic induction in neurons. In this work, we numerically show that the electromagnetic induction phenomenon can firstly suppress chaotic states in a neural setups and secondly enrich neural synchrony in a system of two coupled neurons. By means of the bifurcation diagrams on maximum Lyapunov exponent and interspike interval, we show that increasing in memristor strength delocalizes first, then fully suppresses chaotic states in a single neuron. In a system of two electrically coupled Hindmarsh–Rose-type neurons, we realize that increasing in memristor strength gradually reduces the threshold value of electrical synaptic coupling strength above which a transition to synchronized states is achieved. The transition to synchronized states are determined either by the sign of the maximum transverse Lyapunov exponent or by the magnitude of the synchronization factor. Our results suggest that chaos break in a neurons group by electromagnetic induction phenomenon might automatically release neural synchrony which is involved in information processing and many seizures in the brain.

Certain hybrid prototypes of dispersive optical solitons that we are looking for can correspond to new or future behaviors, observable or not, developed or will be developed by optical media that present the cubic-quintic-septic law coupled, with strong dispersions. The equation considered for this purpose is that of non-linear Schrodinger. The solutions are obtained using the Bogning-Djeumen Tchaho-Kofane method extended to the new implicit Bogning’ functions. Some of the obtained solutions show that their existence is due only to the Kerr law nonlinearity presence. Graphical representations plotted have confirmed the hybrid and multi-form character of the obtained dispersive optical solitons. We believe that a good understanding of the hybrid dispersive optical solitons highlighted in the context of this work allows to grasp the physical description of systems whose dynamics are governed by nonlinear Schrodinger equation as studied in this work, allowing thereby a relevant improvement of complex problems encountered in particular in nonliear optaics and in optical fibers.

Considered under their standard form, the fifth-order KdV equations are a sort of reading table on which new prototypes of higher order solitary waves residing there, have been uncovered and revealed to broad daylight. The mathematical tool that made it possible to explore and analyze this equation is the Bogning-Djeumen Tchaho-Kofane method extended to the new implicit Bogning' functions. The analytical form of the solutions chosen in this manuscript is particular in the sense that it contains within its bosom, a package of solitary waves made up of three solitons, especially, the bright type soliton, the hybrid soliton and the dark type soliton which we estimate capable in their interactions of generating new hybrid or multi-form solitons. Existence conditions of the obtained solitons have been determined. It emerges that, these existence conditions of the chosen ansatz could open the way to other new varieties of fifth-order KdV equations including to which it will be one of the solutions. Some of the obtained solitons are exact solutions. Intense numerical simulations highlighted numerical stability and confirmed the hybrid character of the obtained solutions. These results will help to model new nonlinear wave phenomena, in plasma media and in fluid dynamics, especially, on the shallow water surface.

The dynamics of matter waves in a trapped Bose–Einstein condensate including three-body losses, atomic feeding and quantum fluctuations is investigated theoretically and numerically. We use a generalized variational approach which allows us to express the influence of the condensate parameters on the time evolution of the amplitude, width and chirp, through a set of differential equations. Emphasis is placed on the strength of quantum fluctuations which deeply modifies the wave dynamics. Direct numerical simulations confirm the analytical results. Importantly, we extend numerical experiments and show that the localized modes split into two or three trains of solitary waves which can be controlled by the quantum fluctuations.

Based on the standard Fitzhugh-Nagumo model for myocardial cell excitations and electrical activities, the effect of electromagnetic induction is considered and through which mixed frequencies magnetic radiation is imposed to detect the mode transition. Indeed, time-varying electromagnetic field can be induced when myocardial cell is exposed or surrounded by electromagnetic field and thus the effect of electromagnetic induction should be considered. From the analyzes of sampled series for membrane potentials, the improved model holds many bifurcation parameters and the mode of excitations and electric activities can be detected and observed in larger parameter zones. It is found that apart from exciting a myocardial cell, the mixed frequencies magnetic radiation can promote mode transition to bursting type behavior as the frequency is increased as well as suppress the electrical activities to quiescent state under high intensities magnetic radiations, which are consistent with biological experiments.

We study the dynamic of modulated solitary wave patterns in alpha-helical proteins going beyond the standard nearest-neighbor interaction by taking into account influence of long-range dipole–dipole interactions of the power low type. In particular, self-trapping of amide-I energy quanta or exciton by the induced phonon deformation of the hydrogen-bonded lattice of peptide groups is capable of generating moving solitary waves following the Davydov soliton model. Under the adiabatic approximation, the discrete biexciton system is reduced to two coupled nonlinear Schrodinger equations where the dispersive coefficient depends on the long-range interactions parameter and the coupled term depends on the nonlinear saturation effects. We perform the linear stability analysis of continuous wave solutions of the coupled system. This analysis reveals that both nonlinear saturation and long-range interaction parameters affect the dispersion area. More new analytical multisoliton, bright and dark soliton solutions-like patterns are obtained using extended auxiliary equation method. We also observe the time behavior of modulating bright soliton-like pattern due to the nonlinear saturation and long-range interactions terms through numerical simulations.

We report on the existence and stability of Gaussian-type soliton in the nonlinear Schrodinger (NLS) equation with interplay of cubic–quintic nonlinearity, fourth-order diffraction (FOD) and novel quartic anharmonic parity-time ( $$\mathcal {PT}$$ )-symmetric Gaussian potential. We study numerically the impact of the FOD coefficient on the regions of unbroken/broken linear $$\mathcal {PT}$$ -symmetric phases. In the nonlinear domain, we derive exact soliton solutions of the one-dimensional and two-dimensional cubic–quintic NLS equation with $$\mathcal {PT}$$ -symmetric Gaussian potential and FOD coefficients. Moreover, the stability of the constructed soliton solution is investigated. The results of linear stability analysis are validated by comparison with numerical simulations. Furthermore, we also show that the relative strength of the FOD coefficient influences the direction of the power flow.

The response in terms of probability density function (PDF) of a vibration transducer, whose mechanical and electrical parts are respectively subjected to stochastic force and bounded noise excitation, is revisited in this report, both analytically and numerically. We discuss the phenomenological transitions exhibited by the PDFs as the noisy excitations parameters evolve and analyze the dependence of the mean output power (MOP) on the parameters of noisy excitations. In the weak parameter regime, using the stochastic averaging method, we show that the MOP of the transducer increases with the intensity of the electrical oscillator additive noise; however, it is independent of the mechanical oscillator additive noise intensity. Conversely, in the hard coupling regime, we show, by Monte Carlo simulations, that the PDFs and the MOP are also affected by the mechanical oscillator additive noise parameters. In particular, we find that the system exhibits the stochastic P-bifurcation only for large damping and coupling parameters. The simulations and the approximate analytical treatment are consistent in the weak parameter regime, as expected.

By introducing the relation between the orders of the two independent small expansion parameters, the amplitude parameter α and the long wavelength parameter β , which are taken in the form β = 0 α n and α = 0 β m , with n and m specified to two particular cases, we derive some new higher order partial differential nonlinear evolution equations for unidirectional shallow water waves under the influence of gravity as well as surface tension. We then show that it is possible to construct one-solution which satisfy these estimates using the Hirota’s bilinear method.

In this work, we analyze stabilization of three dimensional spatiotemporal solitons (“dissipative light bullets”) in highly nonlinear doped Kerr media with higher-order dispersion terms. The analytical approach based on variational analysis and numerical simulations shows that dissipative light bullets can be formed for a large range of parameters and can be stabilized under certain conditions. A set of evolution equations and expression for potential function have been derived using variational method. The fixed points are investigated by the means of Lyapunov’s method. We have highlighted the evolution of physical parameters (amplitude, widths, chirps and phase) of the dissipative optical bullets and analyzed their dynamics. A potential well has been generated into a single point due to the exact balance between repulsive and attractive potentials, justifying the stability of the fixed point. As a result, stable and robust dissipative light bullets are formed during a self-organizing propagation due to the cross compensation of various linear and nonlinear effects. Among them, we have stationary dissipative light bullets, bounded by the well known double and quadruple bullet complexes, and the new rich variety of bullet complexes like sixfold, eightfold and tenfold, respectively. Using the natural control parameter of the solution as it evolves, named the total energy Q, we have shown by numerical simulations that, as soon as we evolve from two to ten bullet complexes, the total energy increases considerably and that, for localized solutions with an symmetric initial condition, the energy increases but remains finite and converges to a constant value when a stationary solution is reached. Furthermore, It has been demonstrated in this work that, using an elliptic initial condition, solutions may be stable or unstable.

In this paper, we analyze transport memory effects in bistable reaction − diffusion systems. Traveling wave fronts are obtained for two interesting cases: (i)The nonlinear reaction term is treated without any approximation by factorization method. We find that transport memory effects appear to play a key role as it prevents the concentration or the amplitude from taking negative values. These memory effects enter the dynamics of the reaction diffusion systems through their influence on the speed of the traveling wave fronts. (ii) The nonlinear reaction term is replaced by a piecewise linear approximate form. We obtain a system of differential equations describing the three damped harmonic oscillators, one of which has a negative mass and the others positive masses.

During the propagation of action potential, large extracellular potential as well as the difference in the transmembrane potential between adjacent nerve fibers can induce electromagnetic induction current in the neighboring fibers. This can modify the electrical and excitation behaviors of neighboring nerve fibers resulting in interneuronal communication. In this paper, the FitzHugh–Nagumo model is used to describe the local kinetics of the neuronal network and the memristive electromagnetic induction current is included to approach coupling between adjacent nerve fibers. Modulational instability technique is explored both analytically and numerically to bring out some communication features based on nonlinear structures. Through multiple scale expansion in the discrete approximation limit, we show that the dynamics of the network is governed by a well-known differential-difference nonlinear equation. The stability of the plane wave solution revealed the contribution of memristive electromagnetic induction coupling $$K_{0}$$ in enhancing interneuronal communication. By exploring the long time evolution of the modulated plane wave via numerical experiments using parameters chosen from the unstable parameter region, the initiation and dynamics of the nonlinear structures agree with the analytical predictions. Extensive numerical experiments revealed the possibility of achieving perfect interneuronal communication using a controlled pitch of magnetic radiation. The results can provide guidance in developing therapy for brain seizure.

We report the contrast of optical activity and properties of nonparaxial optical rogue waves for the higher-order nonparaxial chiral nonlinear Schrodinger (NLS) equation. The latter describes the propagation of ultrashort optical pulses in chiral optical fibers. Both first- and second-order rogue wave solutions are investigated analytically by the modified Darboux transformation (MDT) and numerically by one pseudo-spectral method. The interplay of chiral materials on rogue wave propagation is elucidated, and the results can be applied on optical communication and in others physical systems.

We study the dynamics of modulated ionic waves in a microtubule modeled by a nonlinear RLC transmission line (Tuszynski et al., 2004; Sataric et al., 2009). We show through the application of a reductive perturbation technique that the network can be reduced in the continuum limit to the dissipative nonlinear Schrodinger equation. The processes of the modulational instability and the effects of the dissipative elements of the network on wave propagation are investigated. We perform numerical simulations which confirm analytical predictions and give rise to localized modulated wave formation. The results suggest that microtubules can be biological structures where short-duration nonlinear waves called electrical envelope solitons can be created and propagated.

A system for three-strand α -helix proteins, with long-range dispersive interactions among polypeptide units, is considered. The associate improved Davydov model is shown to be fully described by a set of modified coupled discrete nonlinear Schrodinger equations, which involve long-range interactions between peptide groups along the protein strands. By means of the modulational instability theory, the competition between nonlinearity and long-range intermolecular interactions are shown to modify the domain of instability of plane waves. The impact of the competition between nonlinearity and long-range interactions, on the process of energy transport and storage, is also addressed numerically. It is shown that nonlinearity and the long-range couplings conspire to the emergence of trains of solitonic structures, when parameters are well chosen within the domain of instability of plane waves. The relevance of the improved model as well as the biological implications of the account of long-range intermolecular interactions, are discussed in the contexts of energy transport and storage in hydrogen-bonded molecular structures in general, and in α -helix proteins in particular.

This work investigates the ability of a new tuned pendulum mass damper to control the behavior of a structure. A very rich nonlinear dynamics is reached by a mass fixed on a spring and driven by a conveyor belt. That is the stick-slip motion (either regular or chaotic), the chaotic motion and very low amplitude motion. When a control systems like the tuned mass damper are used, the conversion of chaotic stick-slip into regular stick-slip is observed. For certain tuned mass dampers, the regular stick-slip is transformed into a stick-slip with very small amplitude. In addition, the chaotic motion is converted into regular motion, while very low amplitude motion remains unchanged. Very few cases of anti-control have been noted. Thereafter, a comparison on the effectiveness of control systems was made, especially in the case of chaotic motions. For this purpose, the largest Lyapunov exponent is evaluated and the stability map was obtained. It is shown that the best control system depends on the value of the mass ratio between the controller and the structure (which should be as small as possible for civil engineering implementation). In addition, the best control system is closely related to the type of motion considered.

International audience; We consider the nonlinear diffusive Burgers' equation as a model equation for signals propagation on the nonlinear electrical transmission line with intersite nonlinearities. By applying the extend sine-cosine method and using an appropriate modification of the Double-Exp function method, we successfully derived on one hand the exact analytical solutions of two types of solitary waves with strictly finite extension or compact support: kinks and pulses, and on the other hand the exact solution for two interacting pulse solitary waves with compact support. These analytical results indicate that the speed of the pulse compactons doesn't depends explicitly on the pulse amplitude as has been expected for long, but rather on the dc-component associated to this trigonometric solution. More interesting, the interactions between the two pulse compactons induce only a phase shift even though they are close together. These analytical solutions are checked by means of numerical simulations. (c) 2018 Elsevier B.V. All rights reserved.

In this work, a self-sustained generator of pulse signal voltages with compact shape is introduced and investigated. It consists of a coupling between the modified Colpitts oscillator (MCO) and a nonlinear electrical transmission line (NLTL) with the appropriated inter-site nonlinearities, exhibiting pulse signal voltages with compact shape, with interesting properties compared to those of pulse solitons. From the state equations governing the dynamics of the MCO part, and through the bifurcation diagram, we have first shown that the system may exhibit an harmonic solution, in certain domain of the control parameter, useful for exciting the NLTL part. In the parameter where the MCO experiences harmonic oscillations, the conditions for a synchronized dynamics of the two main parts of the device are established. Within these conditions, the system generates a train of compact voltage pulse signals. The generator performances namely the pulse width, the repetition rate and the period of pulse repetition rate are derived analytically, and the results indicate their dependence on the characteristic parameters of the circuit. The results of numerical and Pspice simulations have confirmed the accuracy of the analytical investigations and the capacity of the circuit to work as a generator of these compact pulse signal voltages.

This paper reports the stochastic resonance (SR) phenomenon with memory effects for a Brownian particle in a potential whose shape is subjected to deformation. We model the deformation in the system by the Remoissenet–Peyrard potential and the memory effects by the time-delayed feedback. The question of the possible influence of time-delayed feedback on the occurrence of SR is then of our interest. We examine numerically the effect of feedback strength as well as time delay on SR phenomenon in terms of hysteresis loop area. It is found that time-delayed feedback has a significant effect on SR and can induce double resonances in the system. We show that the properties of SR are varying, depending on interdependence between feedback strength, time delay and shape parameter. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

Compression ignition engine modeling draws great attention due to its high efficiency. However, it is still very difficult to model compression ignition engine due to its complex combustion phenomena. In this work, we perform a theoretical study of steam injection being applied into a single-cylinder four-strokes direct-injection and naturally aspirated compression ignition engine running with diesel and biodiesel fuels in order to improve the performance and reduce NO emissions by using a two-zone thermodynamic combustion model. The results obtained from biodiesel fuel are compared with the ones of diesel fuel in terms of performance, adiabatic flame temperatures, and NO emissions. The steam injection method could decrease NO emissions and improve the engine performances. The results showed that the NO formation characteristics considerably decreased and the performance significantly increased with the steam injection method. The relative errors for computed nitric oxide concentration values of biodiesel fuel and diesel fuel in comparison to the measured ones are 2.8% and 1.6%, respectively. The experimental and theoretical results observed show the highly satisfactory coincidences.

Synchronization of fractional-order-derivative systems for cryptography purpose is still exploratory and despite an increase in cryptography research, several challenges remain in designing a powerful cryptosystem. This chapter addresses the problem of synchronization of fractional-order-derivative chaotic systems using random numbers generator for a novel technique to key distribution in cryptography. However, there is evidence that researchers have approached the problem using integer order derivative chaotic systems. Consequently, the aim of the chapter lies in coding and decoding a text via chaos synchronization of fractional-order derivative, the performance analysis and the key establishment scheme following an application on a text encryption using the chaotic Mathieu-Van Der Pol fractional system. In order to improve the level of the key security, the Fibonacci Q-matrix is used in the key generation process and the initial condition; the order of the derivative of the responder system secretly shared between the responder and the receiver are also involved. It followed from this study that compared to the existing cryptography techniques, this proposed method is found to be very efficient due to the fact that, it improves the key security.

Motivated by the fact that the restrictive conditions for a Turing instability are relaxed in sub- diffusive regime, we investigate the effects of subdiffu- sion in the predator−prey model with toxins under the homogeneous Neumann boundary condition. First, the stability analysis of the corresponding ordinary differ- ential equation is carried out. From this analysis, it fol- lows that stability is closely related to the coefficient of toxicity. In addition, the temporal fractional derivative does not systematically widen the range of parameters to maintain a point in the stability domain. Further- more, we derive the condition which links the Turing instability to the coefficient of toxicity in the subdif- fusive regime. System parameters are varied in order to test our mathematical predictions while comparing them to ecological literature. It turns out that the mem- ory effects, linked to the transport process can, depend- ing on the parameters, either stabilize an ecosystem or make a completely different configuration.

Upon the Joyeux-Buyukdagli model of DNA, the helicoidal interactions are introduced, and their effects on the dynamical behaviors of the molecule investigated. A theoretical framework for the analysis is presented in an external force field, taking into account Stokes and hydrodynamics viscous forces. In the semi-discrete approximation, the dynamics of the molecule is found governed by the cubic complex Ginzburg-Landau (CGL) equation. By choosing an appropriate decoupling ansatz, the cubic CGL equation is transformed into a nonlinear differential equation whose analytical solitary wave-like solutions can be explored by means of the direct method, which is more tractable in case where the form of soliton solutions is known. Based on this, a dissipative bright-like soliton solution is obtained. Numerical experiments have been done, and relevant results were brought out, such as the quantitative and qualitative influences of the helical interactions on the parameters of the traveling bubble. The important role-played by these interactions in the DNA biological processes is brought out, showing that depending on the wave number, their effects can increase, decrease, or keep constant the bubble angular frequency, velocity, amplitude, and width, as well as the energy involved by enzymes in the initiation of DNA biological processes. This can prevent some coding or reading errors and resulting genetic damages. Analytical predictions and numerical experiments were in good agreement.

Pulse propagating in inhomogeneous nonlinear media with linear/nonlinear gain and loss described by the asymmetrical (2 + 1)-dimensional cubic-quintic Ginzburg-Landau equation is considered. The evolution and the stability of the dissipative optical solitons generated from an asymmetric input with respect to two transverse coordinates x and y are studied. Our approach is based on the variational method. This approach allows us to analyze the influence of various physical parameters on the dynamics of the propagating signal and its relevant parameters. According to the parameters of the system and a suitable choice of the test function, a domain of dissipative parameters for stable solitonic solutions is determined. Bifurcation diagrams related to the existence of the stationary solutions presented show a good agreement between analytical and numerical results.

The use of biodiesel fuels in compression ignition engines leads to decrease CO, PM, HC and smoke opacity. However, NOx emissions increase importantly. Various methods to reduce NOx are used namely the EGR, the water injection method and the steam injection method. In this study, the steam injection method has been used instead of the other methods because of its benefits. This study examines the effects of steam injection on combustion products of diesel and biodiesel fuels by considering chemical equilibrium in order to determine the equilibrium combustion products involving 10 combustion products. A developed simulation code determing the equilibrium mole fractions and thermodynamic properties of combustion products is used for diesel and biodiesel fuels. It can be used for any fuel consisting of carbon, hydrogen or any oxygenated fuel. The results show that the mole fraction of CO2 and CO decrease with the steam injection ratios. NO mole fractions decrease with steam injection for lean mixtures but they increase slightly in the case of rich mixtures. The specific heat of combustion products increase with the steam injection ratios. Thus, the engine performance can be improved using the method. The model has been validated by comparing model results with the ones of NASA CEA software and GASEQ software using the methane as fuel. The relative errors of equilibrium mole fractions and thermodynamic properties of combustion products are less than 0.98 %.

Motivated by often non-observance clinical effects attributed to some pathological heart diseases, we obtain in this paper the analytical solutions describing localized nonlinear excitations in an improved diffusive FitzHugh–Nagumo cardiac tissue model. The improved model includes the magnetic flux variable used to describe the effect of electromagnetic induction created by fluctuation in ionic concentration during the period when signals are initiated and propagated in the heart. To be consistent with physical units, memristor is used to achieve coupling between membrane potential and magnetic flux such that the induced current from electromagnetic induction is approached. Using the specific reductive perturbation approach in the semi-discrete approximation limit, we show that the whole system dynamics is governed by a modified complex Ginzburg–Landau equation, whose coefficients are dependent on memristive feedback gain. This suggests from biophysical point of view that cardiac electrical signals or waves initiated from the heart sinus node propagates in cardiac networks both in temporal and spatial dimensions in the form of a localized modulated solitonic wave thereby regulating heartbeat as powerful pacemaker. Our analytical solutions are then verified through numerical experiments.

Modulational instability, as a mechanism of wave trains and soliton formation in biological system, is explored in the frame work of the new FitzHugh–Nagumo model. This model considered chain networks with memristive synaptic connection between adjacent neurons. This connection replaces the synaptic coupling and neurons bridged for signal exchange. From the physical law of electromagnetic induction, we interpret the traditional current term as magnetic flux variable. Magnetic flux is used to describe time-varying electromagnetic field setup in cells as a result of internal bioelectricity of the nervous system as well as when cells are exposed to external electromagnetic field. We reduced the whole network dynamical equations through multi-scale expansion to obtain a single differential–difference nonlinear equation of Schrodinger type. Linear stability is then performed with emphasis on memristive synaptic coupling. The conditions under which uniform plane waves propagating in the network become stable or unstable under small perturbation are calculated and plotted. Numerical experiments confirm our analytical predictions as the network supports localized mode excitations, spike-like, identified as quasi-periodic patterns, with some features of synchronization. It is confirmed that under strong electromagnetic radiation, the propagating waves encountered turbulent electrical activities, with patterns breakdown into a homogeneous state. This disordered state, collapse and instability of traveling pulse are monitored and analyzed using the sampled time series for membrane potential. It decreases to quiescent state under strong electromagnetic field. This could provide some guidance to understanding some neurodegenerative manifestations linked with high radiation exposure.

The internal mobility of the DNA molecule, in a weakly damped medium, is studied. Inspired by the microscopic Peyrard-Bishop-Dauxois model, a zigzag model, which considers longitudinal and transverse vibrations of base pairs is used. The damped limit is considered and the whole system is shown to be governed by a dissipative nonlinear Schrodinger equation. The linear stability analysis of a plane wave solution is thereafter performed. The oscillations and open states of the DNA duplex are also addressed, where two hyperbolic functions are used to construct DNA bubbles in the form of bright- and kink-type soliton solutions. The confirmation of analytical predictions is verified through direct numerical experiments. There are good accuracy and good agreement between the quantitative and qualitative influence of damping forces on the width and amplitude of the moving soliton. Such relevant results could be used to predict the generation of moving bubbles along the DNA molecule, and to explain energy transfer and localization processes during the fundamental processes of DNA replication and transcription.

We investigate the propagation characteristics and stabilization of generalized-Gaussian pulse in highly nonlinear homogeneous media with higher-order dispersion terms. The optical pulse propagation has been modeled by the higher-order (3+1)-dimensional cubic–quintic–septic complex Ginzburg–Landau [(3+1)D CQS-CGL] equation. We have used the variational method to find a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links. The variational equations we obtained have been integrated numerically by the means of the fourth-order Runge–Kutta (RK4) method, which also allows us to investigate the evolution of the generalized-Gaussian beam and the pulse evolution along an optical doped fiber. Then, we have solved the original nonlinear (3+1)D CQS-CGL equation with the split-step Fourier method (SSFM), and compare the results with those obtained, using the variational approach. A good agreement between analytical and numerical methods is observed. The evolution of the generalized-Gaussian beam has shown oscillatory propagation, and bell-shaped dissipative optical bullets have been obtained under certain parameter values in both anomalous and normal chromatic dispersion regimes. Using the natural control parameter of the solution as it evolves, named the total energy Q , our numerical simulations reveal the existence of 3D stable vortex dissipative light bullets, 3D stable spatiotemporal optical soliton, stationary and pulsating optical bullets, depending on the used initial input condition (symmetric or elliptic).

This paper presents many new solutions of a modified Zakharov–Kuznetsov equation obtained by using the Jacobi elliptical function method. This equation is shown to model a two dimensional discrete electrical lattice. The solutions reported herein are of varied types and include hyperbolic and trigonometric solutions, as well as kink and bell-shaped solitons. The comparison of our results to well-known ones is done. The method used here is very simple and concise and can be also applied to other nonlinear partial differential equations. More importantly, the solutions found in this work can have significant applications in telecommunication systems where solitons are used to codify data.

In this work, we aimed at analyzing the wind speed of Faya-Largeau and making decisions of the cost effective wind turbine for the said zone. The characteristics of the wind speed and the energy potential of Faya-Largeau in the Saharan zone of Chad were studied using monthly wind speed data collected over eighteen years (1960–1978) and measured at 10 m height. In order to determine the wind power density and the available energy for the Faya-Largeau site in the Saharan zone of Chad, the Weibull probability density function was used. Thus, the annual values of the Weibull parameters k and c are respectively 3.75 and 3.60 (m/s), whereas the power density and available energy are respectively 343.31 W/m2 and 249.87 kWh/m2. Three commercial wind turbine models were used. Based on the capacity factor, the 1.MW/54 Bonus model is cost-effective for the Faya-Largeau site and could be strongly recommended for installation.

In this paper, thermodynamics and phase transition are investigated for the regular Bardeen black hole surrounded by quintessence. Considering the metric of the Bardeen spacetime surrounded by quintessence, we derived the Unruh-Verlinde temperature. Using the first law of thermodynamics, we derived the expressions of the Hawking temperature as well as the specific heat for the black hole. Explicitly, their behaviors were plotted. It results that the magnetic monopole charge β as well as the presence of quintessence decrease the temperature and induce a thermodynamics phase transition in the spacetime. Moreover, when increasing the density of quintessence, the transition point moves to lower entropies.

Objective: To Study the photo-electric behavior of Spinacea pleracea by using the T.E-model of chlorophyll pigment. Methods/Statistical Analysis: The technic and method employed consisted on modeling the chlorophyll as an electrical circuit, to make a statistical analysis of electric conductance process of S. pleracea in light and in darkness by evaluating, the statistical average and statistical autocorrelation function, and make a temporal analysis by evaluating, the temporal average and temporal autocorrelation function. Finding: The electric conductance of Spinacea pleracea leaf plant increases when one passes from darkness to light; the spectral density of power (DSP) of the electric conductance process G(ω,t) under darkness is up to the DSP of the signal when S. pleracea is under light for the whole value of the reduced normalized frequency; the process is non-statistics in the broad sense (SSL) and non ergotic. The resemblance of the flow charge evaluated by autocorrelation functions for different values of the shift parameter is higher in light than in darkness. Application/Improvements: This study provided an additional tool to have an idea about the state of reactional center of photosystem II, knowing that the fluorescence emission testifies the loss of energy during the transfer of excitation to the reactional centers. In the same way, the electric conductance testifies the transfer of electrons released from the special chlorophyll ‘a’ of the reactional center to the photosynthetic channel. Keywords: Chlorophyll, Ergotic, Spectral Density of Power (DSP), Spinacea pleracea, Statistics in the Broad Sense (SSL)

Understanding the effects of anisotropy and substrate shape on the stochastic processes is critically needed for the improvement of the quality of the transport information. The effect of biharmonic force on the transport phenomena of a particle in two-dimensional is investigated in the framework of three representative substrate lattices: NaCl, Mo S 2 and honeycomb. We focus on the particles drift velocity, to characterize the transport properties in the system. Normal and anomalous transport are identified for a particular set of the system parameters such as the biharmonic parameter, the bias force, the phase-lag of two signals, as well as the noise amplitude. According to the direction ψ where the bias force is applied, we determine the biharmonic parameter ϵ for the presence of anomalous transport and show that for the NaCl surface, the anomalous transport is observed for 2 ϵ 10 . For the Mo S 2 surface, it appears at monochromatic driven ( ϵ = 0 ) and for 3 ϵ 9 . In particular for the honeycomb surface anomalous transport is generated for 0 ⩽ ϵ 6 only when ψ > 30 ° .