The study of phase portraits, multistability visualization, Lyapunov exponents and chaos identification of coupled nonlinear volatility and option pricing model

Jhangeer, Adil; Faridi, Waqas Ali; Alshehri, Mansoor

doi:10.1140/epjp/s13360-024-05435-1

Eur. Phys. J. Plus

2024

DOI: 10.1140/epjp/s13360-024-05435-1

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The study of phase portraits, multistability visualization, Lyapunov exponents and chaos identification of coupled nonlinear volatility and option pricing model

Adil Jhangeer,

Waqas Ali Faridi,

Mansoor Alshehri

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Cited by 6 publications

References 36 publications

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Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system

Younas,

Hussain,

Muhammad

et al. 2025

Ain Shams Engineering Journal

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Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system

Younas,

Hussain,

Muhammad

et al. 2025

Ain Shams Engineering Journal

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Bifurcation, chaotic behaviors and solitary wave solutions for the fractional Twin-Core couplers with Kerr law non-linearity

Li,

Lyu,

Hussain

2024

Sci Rep

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The main purpose of this article is to analyze the bifurcation, chaotic behaviors, and solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity by using the planar dynamical system method. This equation has profound physical significance and application value in the areas of optics and optical communication. Firstly, the traveling wave transformation is applied to convert the beta-derivative Twin-Core couplers with Kerr law non-linearity into the ordinary differential equations. Secondly, phase portraits and Poincaré sections of two-dimensional dynamical system and its perturbation system are plotted by using mathematical software. For different initial values, the planar phase diagram and three-dimensional phase diagram in red and blue are plotted, respectively. Finally, the solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity are obtained by using theory of planar dynamical system. In addition, three-dimensional graphs, two-dimensional graphs, and the contour graphs of the solitary wave solutions are drawn.

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The profile of soliton molecules for integrable complex coupled Kuralay equations

Hussain,

Ibrahim,

Bashier

et al. 2024

Phys. Scr.

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This study focuses on mathematically exploring the Kuralay equation, which is applicable in diverse fields such as nonlinear optics, optical fibers, and ferromagnetic materials. This study aims to investigate various soliton solutions and analyze the integrable motion of the induced space curves. This study employs traveling wave transformation, converting the partial differential equation (PDE) into an ordinary differential equation (ODE). Soliton solutions are derived utilizing both the generalized Jacobi elliptic function expansion (JEFE) method and novel extended direct algebraic (EDA) methods. The outcomes encompass a diverse range of soliton solutions, including double periodic waves, shock wave solutions, kink-shaped soliton solutions, solitary waves, bell-shaped solitons, and periodic wave solutions, obtained using Mathematica. In contrast, the EDA method produces dark, bright, singular, combined dark-bright solitons, dark-singular combined solitons, solitary wave solutions, etc. Visual representation of these soliton solutions is accomplished through 3D, 2D, and contour graphics, with a meticulous selection of parametric values. The graphical presentation underscores the influence of the parameters on the soliton propagation.

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The study of phase portraits, multistability visualization, Lyapunov exponents and chaos identification of coupled nonlinear volatility and option pricing model

Cited by 6 publications

References 36 publications

Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system

Bifurcation analysis, chaotic behavior, sensitivity demonstration and dynamics of fractional solitary waves to nonlinear dynamical system

Bifurcation, chaotic behaviors and solitary wave solutions for the fractional Twin-Core couplers with Kerr law non-linearity

The profile of soliton molecules for integrable complex coupled Kuralay equations

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