Fractional unstable patterns of energy in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si15.gif" overflow="scroll"><mml:mrow><mml:mi>α</mml:mi><mml:mo>−</mml:mo></mml:mrow></mml:math>helix proteins with long-range interactions

Tabi, Conrad Bertrand

doi:10.1016/j.chaos.2018.09.037

Cited by 18 publications

(4 citation statements)

References 37 publications

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“…For instance, it has been well established that they may appear in physical systems as the consequence of the interplay between nonlinear and dispersive effects, under the activation of the so-called MI phenomenon [3][4][5][6][7][8]. Recently, interest in studying RWs has gone beyond oceanography and hydrodynamics [9,10] to reach some other areas related to optics and photonics [11][12][13][14], Bose-Einstein condensation [15][16][17], biophysics [18][19][20][21], plasma physics [22,23], just to name a few. Particularly, ion-acoustic super-RWs were found in an ultra-cold neutral plasma in the presence of ion-fluid and nonextensive electron distribution [24].…”

Section: Introductionmentioning

confidence: 99%

Low relativistic effects on the modulational instability of rogue waves in electronegative plasmas

2019

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Relativistic ion-acoustic waves are investigated in an electronegative plasma. The use of the reductive perturbation method summarizes the hydrodynamic model to a nonlinear Schrödinger equation which supports the occurrence of modulational instability (MI). From the MI criterion, we derive a critical value for the relativistic parameter 1 , below which MI may develop in the system. The MI analysis is then conducted considering the presence and absence of negative ions, coupled to effects of relativistic parameter and the electron-to-negative ion temperature ratio. Under high values of the latter, additional regions of instability are detected, and their spatial expansion is very sensitive to the change in 1 and may support the appearance of rogue waves whose behaviors are discussed. The parametric analysis of super-rogue wave amplitude is performed, where its enhancement is debated relatively to changes in 1 , in the presence and absence of negative ions.

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Section: Introductionmentioning

confidence: 99%

Low relativistic effects on the modulational instability of rogue waves in electronegative plasmas

2019

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“…More recently, chaotic poles of attraction were studied in the Hindmarsh-Rose model in presence of fractional-order derivatives, using the Haar wavelet technique [14]. The one proposed by Caputo has been widely studied in the literature and summarizes fractional-order derivatives in the form [6,3,39]…”

Section: 1mentioning

confidence: 99%

Stochastic dynamics of the FitzHugh-Nagumo neuron model through a modified Van der Pol equation with fractional-order term and Gaussian white noise excitation

Guimfack¹,

Tabi²,

Mohamadou³

et al. 2021

DCDS-S

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The stochastic response of the FitzHugh-Nagumo model is addressed using a modified Van der Pol (VDP) equation with fractional-order derivative and Gaussian white noise excitation. Via the generalized harmonic balance method, the term related to fractional derivative is splitted into the equivalent quasi-linear dissipative force and quasi-linear restoring force, leading to an equivalent VDP equation without fractional derivative. The analytical solutions for the equivalent stochastic equation are then investigated through

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“…Solitons are waves that can propagate over long distances without any twist and can preserve their shapes [25]. More precisely solitons are usually resulting from the confrontation between nonlinear and dispersions terms However, solitons propagation is described by nonlinear evolution equations such as NLSE, nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves, the dissipative Kuramoto-Sivashinsky equation, the perturbed Chen-Lee-Liu equation, the fractional second and third-order nonlinear Schrödinger equation, the complex Swift-Hohenberg equation, the space-time fractional nonlinear Schrödinger equation, the high-order nonlinear Schrödinger equation, the specific coupled nonlinear Schrödinger equations, just to name a few [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Owing to the nonlinear term of the NLSE, diverse forms are known in literature such as Kerr law, Cubic-Quintic Nonlinearity (CQN), parabolic law including saturable nonlinearity [7,[12][13][14]22].…”

Section: Introductionmentioning

confidence: 99%

“…In [28,29], it has been shown how the saturation terms can deeply affect the MW and modulation bands in bi-exciton alpha-helical protein chains. MI is the powerful method where the confrontation between dispersion and nonlinearity terms is exhibited by using the small perturbations of the continuous waves (CWs) [3,7].…”

Section: Introductionmentioning

confidence: 99%

Modulation instability gain and modulated wave shape incited by the acoustic longitudinal vibrations in molecular chain model

Houwe¹,

Saliou²,

Djorwé³

et al. 2022

Phys. Scr.

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The propagation of the modulated wave pattern and its instability in the nonlinear medium is an important study from where experimental results are obtained. In this work, we use the nonlinear Schrödinger equation (NLSE) with saturation nonlinearity which describes the solitonic waves in the molecular chain model. We set our study on the eﬀectiveness of the acoustic longitudinal velocity which is related to the acoustic longitudinal vibration to investigate the behavior of the modulated wave patterns as well as the modulation instability (MI) gain. Its results are that the acoustic longitudinal velocity creates instability zones, increases MI bands, and shortens the transition regime of the modulated wave pattern. For a long time of simulation and a great enough value of the acoustic longitudinal velocity, the modulated waves feature chaos-like motion. Alongside these results the acoustic longitudinal velocity obvious itself as tool control of modulated wave as well as an energy source for the propagation of diverse modulated wave-shaped in the molecular chain.

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Fractional unstable patterns of energy in α−helix proteins with long-range interactions

Cited by 18 publications

References 37 publications

Low relativistic effects on the modulational instability of rogue waves in electronegative plasmas

Low relativistic effects on the modulational instability of rogue waves in electronegative plasmas

Stochastic dynamics of the FitzHugh-Nagumo neuron model through a modified Van der Pol equation with fractional-order term and Gaussian white noise excitation

Modulation instability gain and modulated wave shape incited by the acoustic longitudinal vibrations in molecular chain model

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