Dynamics of modulated waves in a lossy modified Noguchi electrical transmission line

Kengne, Emmanuel; Lakhssassi, Ahmed; Liu, W. M.

doi:10.1103/physreve.91.062915

Cited by 23 publications

(5 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result is in perfect agreement with existing results on the dissipative NLTL in which the dissipative terms of the NLS equation disappear when the dissipation elements (resistances) are not considered. [30][31][32] However, in contrast to these previous results, the dissipation is not neglected in the model studied in this paper. In other words, the resistance (R) always exists in our system but its effect is counterbalanced by the effect of the nonlinear conductance J.…”

Section: Extended Nonlinear Schrödinger Equationmentioning

confidence: 76%

See 1 more Smart Citation

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

et al. 2023

View full text Add to dashboard Cite

In this paper, the control of dissipation and amplification of solitary waves in an electrical model of microtubule is demonstrated. This model is consisted of a shunt nonlinear resistance-capacitance ($J(V)-C(V)$) circuit and a series resistance-inductance $(R-L$) circuit. Through the linear dispersion analysis, two characters of the network are found, that is low band pass and bandpass characters. The effects of the conductance's parameter $\lambda$ on the linear dispersion curve are also analyzed. It appears that the increase of $\lambda$ induces a decrease (an increase) of the width of the bandpass filter for positive (negative) values of $\lambda$. By applying the reductive perturbation method, we derive the equation governing the dynamics of the modulated waves in the system. This obtained equation is the well-known nonlinear Schrödinger equation extended by a linear term proportional to an hybrid parameter $\sigma$, i.e. dissipation or amplification coefficient. Based on this parameter, we successfully demonstrate the hybrid behavior (dissipation and amplification) of the system. The exact and approximate solitary wave solutions of the obtained equation are derived and the effects of the coefficient $\sigma$ on the characteristic parameters of these waves are investigated. Using the found analytical solutions, we show numerically that the waves that are propagated throughout the system can be dissipated, amplified, or remained stable depending on the network parameters. These results are not only in agreement with the analytical predictions, but also with the existing experimental results in the literature.

show abstract

Section: Extended Nonlinear Schrödinger Equationmentioning

confidence: 76%

“…Indeed, it is well known that the kind of solutions the NLS equation has strongly depends on the sign of the product of these parameters. [30][31][32]…”

Section: Extended Nonlinear Schrödinger Equationmentioning

confidence: 99%

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

et al. 2023

View full text Add to dashboard Cite

show abstract

“…DNLS equation also finds numerous application in the transmission of light pulses down an optical fiber, phase transitions in materials, and modeling of signals in real electrical lattices. [35][36][37][38]…”

Section: Nerve Transmission Line Model Equations Of the Electrical La...mentioning

confidence: 99%

“…We assume that Eq. ( 29) possesses a solution of the form [37] u(X) = sech(mX), (30) where m and ρ(τ 2 ) are parameters to be determined. By substituting Eq.…”

Section: Modulational Instability Analysis and The Observation Of Loc...mentioning

confidence: 99%

Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane

2023

View full text Add to dashboard Cite

We systematically study the evolution of modulated nerve impulses in a myelinated nerve fiber, where both the ionic current and membrane capacitance provides the necessary nonlinear feedbacks. This is achieved by using a perturbation technique, in which the Liénard form of the modified discrete Fitzhugh-Nagumo equation is reduced to the complex Ginzburg-Landau amplitude equation. Three distinct values of the capacitive feedback parameter are considered. At the critical value of the capacitive feedback parameter, it is shown that the dynamics of the system is governed by the dissipative nonlinear Schrödinger equation. Linear stability analysis of the system depicts the instability of plane waves, which is manifested as burst of modulated nerve impulses that fulfills the Benjamin-Feir criteria. Variations of the capacitive feedback parameter generally influences the plane wave stability and hence the type of wave profile identified in the neural network. Results of numerical simulations mainly confirms the propagation, collision, and annihilation of nerve impulses in the myelinated axon.

show abstract

“…The transmission line is a particular medium intended for carrying alternating radiofrequency current and its exact solutions include applications in phase shifters in phased antenna arrays, radio transmitters, and receivers, High-speed digital data buses, cell network systems, frequency multipliers, computer network links. The NETL equations have been shown to be a good example for studying the propagation of electrical solitons in nonlinear dispersive media that can generate voltage waves to model the exotic properties of novel systems in many studies [15][16][17][18][19][20][21][22][23][24]. A nonlinear model of low-pass electrical transmission lines is specified as [9] ( ) ( ) ( )…”

Section: Introductionmentioning

confidence: 99%

Construction of new traveling and solitary wave solutions of a nonlinear PDE characterizing the nonlinear low-pass electrical transmission lines

Kumar¹,

Kumar²,

Chand³

et al. 2021

Phys. Scr.

View full text Add to dashboard Cite

In this study, we intend to analyze the traveling and several other solitary wave solutions in the nonlinear low-pass electrical transmission line model using the new mapping method, the new extended auxiliary equation method, and the extended Kudryashov method. A type of traveling and solitary wave solutions emerge, consisting of hyperbolic function, trigonometric, rational, periodic, and doubly periodic solutions that reflect kink, anti-kink wave solitons, bright-dark optical solitons, singular solitons, and other traveling waves. The three integration techniques applied are efficient, effective, and versatile for the creation of new bright, dark, singular, and non-singular periodic and solitary wave propagation solutions in nonlinear low-pass electrical transmission lines. To see the extant physical significance of the considered equation, we present some 2D and 3D figures for some solutions. We compare the obtained results with those obtained in the literature. We investigate and demonstrate the stability of the soliton solutions.

show abstract

Dynamics of modulated waves in a lossy modified Noguchi electrical transmission line

Cited by 23 publications

References 27 publications

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane

Construction of new traveling and solitary wave solutions of a nonlinear PDE characterizing the nonlinear low-pass electrical transmission lines

Contact Info

Product

Resources

About