Multistability and dynamic behavior of non-linear wave solutions for analytical kink periodic and quasi-periodic wave structures in plasma physics

Jhangeer, Adil; Muddassar, Muhammad; Rehman, Zia ur; Awrejcewicz, Jan; Riaz, Muhmmad Bilal

doi:10.1016/j.rinp.2021.104735

Cited by 19 publications

(7 citation statements)

References 37 publications

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“…It can also illustrate clearly the evolution of the nonlinear system for a small change in the value of the control parameter. The study of nonlinear excitations of electrostatic disturbances in the frame work of bifurcation technique and phase portrait analysis has recently received considerable attention [50][51][52][53][54][55][56][57][58][59][60]. Misra et al [50] investigated the saddle-node bifurcation and modulational instability associated with the pulse propagation of nonlinear waves in dissipative dusty plasma.…”

Section: + -mentioning

confidence: 99%

“…They applied the phase portrait analysis, and studied the transition between ion acoustic supersolitons and regular solitary waves. Also, Jhangeer et al [58] studied multistability and bifurcation behavior of periodic and quasi-periodic disturbances in the plasma system. They investigated different kinds of cyclic firing diagram from saddle-node bifurcations.…”

Section: + -mentioning

confidence: 99%

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Normal form for bifurcations of ion acoustic traveling waves in positive-negative ion species plasmas

Alinejad,

Poria

2023

Phys. Scr.

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The normal form for saddle-node and transcritical bifurcation of nonlinear ion-acoustic waves is derived in complex negative-positive plasmas. The physical parameters of four different kinds of multi-ion plasmas which mainly comprise of positive ions (i.e., Xe+ and Ar+) with a minority constituent of negative ions (i.e., SF-6 and F-), inspired from the experimental studies, are examined on the types of bifurcations and nonlinear wave proﬁles. We ﬁnd that such multi-ion plasmas admit transcritical bifurcation preceding the onset of saddle-node bifurcation. The fractional concentration of negative ions controls the dynamics of ion acoustic traveling waves and causes the appearance of solitary structures and supernonlinear periodic waves. When two nonlinear waves disappear via a saddle-node bifurcation on increasing the negative ion concentration, a nonlinear periodic wave is formed. Further, we reveal critical values of ion density marking the transition between nonlinear modes. Such critical points that can be detected analytically give rise to the propagation of new solitary structures. The results obtained here not only limited to laboratory plasmas, but can also be applied to explain wave excitations in space plasma environments.

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Section: + -mentioning

confidence: 99%

Section: + -mentioning

confidence: 99%

Normal form for bifurcations of ion acoustic traveling waves in positive-negative ion species plasmas

Alinejad,

Poria

2023

Phys. Scr.

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“…Turing systems appear in various biological systems, such as patterns in fish, butterflies, lady bugs, tumor growth and synthetic bacterial population (Shin et al, 2014). We can mention the Gierer-Meinhardt model for pattern formation of spatial tissue structures in morphogenesis (Gierer and Meinhardt, 1972), the morphodynamic (limit) model in describing the cell dynamics and the chemical processes during limb bud formation (Alber et al, 2008) and the FitzHugh-Nagumo model for analyzing various processes in the myocardium (Jhangeer et al, 2021;Pavel'chak, 2011;Yasin et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

A reduced-order Jacobi spectral collocation method for solving the space-fractional FitzHugh–Nagumo models with application in myocardium

Abbaszadeh,

Bagheri Salec,

Kamel Abd Al-Khafaji

2023

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PurposeThe space fractional PDEs (SFPDEs) play an important role in the fractional calculus field. Proposing a high-order, stable and flexible numerical procedure for solving SFPDEs is the main aim of most researchers. This paper devotes to developing a novel spectral algorithm to solve the FitzHugh–Nagumo models with space fractional derivatives.Design/methodology/approachThe fractional derivative is defined based upon the Riesz derivative. First, a second-order finite difference formulation is used to approximate the time derivative. Then, the Jacobi spectral collocation method is employed to discrete the spatial variables. On the other hand, authors assume that the approximate solution is a linear combination of special polynomials which are obtained from the Jacobi polynomials, and also there exists Riesz fractional derivative based on the Jacobi polynomials. Also, a reduced order plan, such as proper orthogonal decomposition (POD) method, has been utilized.FindingsA fast high-order numerical method to decrease the elapsed CPU time has been constructed for solving systems of space fractional PDEs.Originality/valueThe spectral collocation method is combined with the POD idea to solve the system of space-fractional PDEs. The numerical results are acceptable and efficient for the main mathematical model.

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“…[41][42][43][44] The most of these studies on the nonlinear waves and existence domains of disturbances have been based on the frame work of phase portraits analysis and bifurcation techniques. [34,[45][46][47][48][49][50][51][52][53][54][55] Misra et al [45] investigated the occurrence of saddle-node bifurcation and modulational instability associated with the envelope solitons in viscous dusty plasma. Rufai et al [46] studied finite amplitude nonlinear ion-acoustic structures in a magnetized two component auroral plasma.…”

Section: Introductionmentioning

confidence: 99%

“…They showed the existence domain of an ion‐acoustic supersoliton and its transition to a regular kind of solitary wave. In addition, Jhangeer et al [ 53 ] investigated the stability and dynamic behaviour of nonlinear wave solutions for analytical periodic and quasi‐periodic wave forms in the plasma system.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation analysis of low‐frequency electrostatic waves in warm negative ion plasmas

Alinejad

2022

Contributions to Plasma Physics

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In this paper, we perform stability and bifurcation analysis of ion-acoustic waves in a plasma consisting of warm adiabatic positive and negative ions, evolving against a uniform background of isothermal electrons. The model consists of two nonlinear ordinary differential equations incorporating ion temperature, negative ion concentration and negative-to-positive ion mass. We derive the normal form of bifurcation which allows the determination of travelling wave solutions for various regions in the parameter space of warm negative ion plasmas. It is shown that negative/positive ion temperature broadens the region prior to the saddle-node bifurcation, thereby allowing the propagation of solitary and supernonlinear periodic waves. For a range of ion mass ratio and ion temperature, we find different existence domains of stability region, and examine the occurrence of transcritical bifurcation as a function of various plasma parameters.Further, we perform a numerical phase portrait analysis of the complex system including homoclinic orbits, nonlinear periodic and super nonlinear periodic orbits. The effects of ion mass ratio and ion temperature on the characteristic of these nonlinear structures are discussed in detail. Our results are relevant to wave solutions in laboratory and space plasmas, where simultaneous presence of warm negative/positive ions are observed.

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Multistability and dynamic behavior of non-linear wave solutions for analytical kink periodic and quasi-periodic wave structures in plasma physics

Cited by 19 publications

References 37 publications

Normal form for bifurcations of ion acoustic traveling waves in positive-negative ion species plasmas

Normal form for bifurcations of ion acoustic traveling waves in positive-negative ion species plasmas

A reduced-order Jacobi spectral collocation method for solving the space-fractional FitzHugh–Nagumo models with application in myocardium

Stability and bifurcation analysis of low‐frequency electrostatic waves in warm negative ion plasmas

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