Bifurcation analysis, chaotic behaviors, sensitivity analysis, and soliton solutions of a generalized Schrödinger equation

Hosseini, K.; Hınçal, Evren; Ilie, Mousa

doi:10.1007/s11071-023-08759-2

Cited by 58 publications

(4 citation statements)

References 34 publications

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“…In the current section, we analyze Equation ( 4) within the framework of bifurcation analysis [20][21][22]. Upon employing the Galilean transformation to Equation (10), we derive the planar system as follows:…”

Section: Bifurcation Phenomenamentioning

confidence: 99%

“…In this section, we introduce an outward periodic force into system (34) to examine the dynamics of both quasi-periodic and chaotic phenomena [20][21][22]. The modified system can be expressed in the following manner:…”

Section: Chaotic Phenomenamentioning

confidence: 99%

“…In this section, we investigate how the suggested equation responds to changes in initial conditions [22,23]. To evaluate the sensitivity of the model, we analyze three distinct sets of initial conditions.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…Similarly, Rafiq et al [21] investigated the qualitative nature of shallow water equations, uncovering multiwave solitons. Additionally, Hosseini et al [22] analyzed the dynamic characteristics of the Schrödinger equation. The chaotic phenomena of the suggested equation is analyzed through the presentation of two-dimensional plots, time plots, and Lyapunov exponents analysis.…”

Section: Introductionmentioning

confidence: 99%

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Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3 + 1)-Dimensional Wave Equation

Riaz,

Jhangeer,

Duraihem

et al. 2024

Symmetry

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The examination of new (3 + 1)-dimensional wave equations is undertaken in this study. Initially, the identification of the Lie symmetries of the model is carried out through the utilization of the Lie symmetry approach. The commutator and adjoint table of the symmetries are presented. Subsequently, the model under discussion is transformed into an ordinary differential equation using these symmetries. The construction of several bright, kink, and dark solitons for the suggested equation is then achieved through the utilization of the new auxiliary equation method. Subsequently, an analysis of the dynamical nature of the model is conducted, encompassing various angles such as bifurcation, chaos, and sensitivity. Bifurcation occurs at critical points within a dynamical system, accompanied by the application of an outward force, which unveils the emergence of chaotic phenomena. Two-dimensional plots, time plots, multistability, and Lyapunov exponents are presented to illustrate these chaotic behaviors. Furthermore, the sensitivity of the investigated model is executed utilizing the Runge–Kutta method. This analysis confirms that the stability of the solution is minimally affected by small changes in initial conditions. The attained outcomes show the effectiveness of the presented methods in evaluating solitons of multiple nonlinear models.

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Section: Bifurcation Phenomenamentioning

confidence: 99%

Section: Chaotic Phenomenamentioning

confidence: 99%

Section: Sensitivity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3 + 1)-Dimensional Wave Equation

Riaz,

Jhangeer,

Duraihem

et al. 2024

Symmetry

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A Framework to Use Bifurcation Analysis for Insight into Complex Systems Resilience

Otalvaro,

Watson

2024

INCOSE International Symp

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The increasing complexity and integration of systems present challenges in understanding and managing these systems, as highlighted by the INCOSE Systems Engineering Vision for 2035. This complexity risks system failures due to insufficient understanding. Resilience Engineering is a field that focuses on system behavior in the face of disruptions. However, existing methods to measure resilience, such as probability‐based measures and linear recovery models, are limited by the non‐linear and dynamic nature of modern systems. Bifurcation Analysis, a mathematical system dynamics technique, offers a different perspective by examining how systems behave under changing conditions. This approach, developed in ecology and traditionally applied in fields including power systems and neural networks, can provide insights into the resilient characteristics of non‐linear systems. Despite its promise, Bifurcation Analysis is not usually associated with Resilience Engineering. This paper proposes using Bifurcation Analysis to understand system resilience better and support Resilience Engineering practitioners. It aims to bridge the gap between the two fields, offering a framework for integrating both approaches. This framework is then applied to a model system to demonstrate its potential to enhance the understanding of system resilience. Contributions are an overview of current Resilience Engineering and Bifurcation Analysis, a general‐use framework for practitioners, and an application of this framework. Future work will focus on applying the new framework to more cases, allowing for improved Resilience Engineering, and improving the framework to make it more accessible, versatile, and reliable.

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Bifurcation Analysis, Sensitivity Analysis, and Jacobi Elliptic Function Structures to a Generalized Nonlinear Schrödinger Equation

Hosseini,

Hinçal,

Alizadeh

et al. 2024

Int J Theor Phys

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Bifurcation analysis, chaotic behaviors, sensitivity analysis, and soliton solutions of a generalized Schrödinger equation

Cited by 58 publications

References 34 publications

Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3 + 1)-Dimensional Wave Equation

Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3 + 1)-Dimensional Wave Equation

A Framework to Use Bifurcation Analysis for Insight into Complex Systems Resilience

Bifurcation Analysis, Sensitivity Analysis, and Jacobi Elliptic Function Structures to a Generalized Nonlinear Schrödinger Equation

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