Bifurcations, chaotic behavior, sensitivity analysis, and various soliton solutions for the extended nonlinear Schrödinger equation

Boundary Value Problems, Journal Year: 2024, Volume and Issue: 2024(1)

Published: Jan. 19, 2024

Abstract In this manuscript, our primary objective is to delve into the intricacies of an extended nonlinear Schrödinger equation. To achieve this, we commence by deriving a dynamical system tightly linked equation through Galilean transformation. We then employ principles from planar systems theory explore bifurcation phenomena exhibited within derived system. investigate potential presence chaotic behaviors, introduce perturbed term and systematically analyze This investigation further enriched presentation comprehensive two- 3D phase portraits. Moreover, conduct meticulous sensitivity analysis using Runge–Kutta method. Through analytical process, confirm that minor fluctuations in initial conditions have only minimal effects on solution stability. Additionally, utilize complete discrimination polynomial method construct single traveling wave solutions for governing model.

Language: Английский

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Investigation of the hyperchaos and control in the fractional order financial system with profit margin

Partial Differential Equations in Applied Mathematics, Journal Year: 2024, Volume and Issue: 9, P. 100612 - 100612

Published: Jan. 6, 2024

This research study proposes a novel hyperchaotic finance system with profit margin and then utilizes the Adomian Decomposition Method (ADM) to tackle solution of associated Caputo-derivative based fractional-order margin. Numerical simulations analyses, such as evaluation Lyapunov exponents (LE), creation bifurcation diagrams (BD), complexity analysis (CA), 0-1 test, are used get full picture system. The results our demonstrate occurrence periodic, chaotic, dynamics in Furthermore, overall criteria for existence uniqueness exact solutions Caputo models presented. In addition, we present control methodology financial utilizing Laplace transform linear feedback control. Significantly, showcases noteworthy correlation between analytical numerical simulations, emphasizing soundness effectiveness methodology.

Language: Английский

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Hidden chaotic attractors and self-excited chaotic attractors in a novel circuit system via Grünwald–Letnikov, Caputo-Fabrizio and Atangana-Baleanu fractional operators

Alexandria Engineering Journal, Journal Year: 2025, Volume and Issue: 116, P. 525 - 534

Published: Jan. 7, 2025

Language: Английский

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Glucose-insulin regulatory system: Chaos control and stability analysis via Atangana–Baleanu fractal-fractional derivatives

Alexandria Engineering Journal, Journal Year: 2025, Volume and Issue: 122, P. 77 - 90

Published: March 12, 2025

Language: Английский

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Qualitative financial modelling in fractal dimensions

Financial Innovation, Journal Year: 2025, Volume and Issue: 11(1)

Published: Jan. 13, 2025

Abstract The Black–Scholes equation is one of the most important partial differential equations governing value financial derivatives in markets. model for pricing stock options has been applied to various payoff structures, and trading based on Black Scholes’ principle dynamic hedging estimate assess option prices over time. However, requires severe constraints, assumptions, conditions be real-life economic problems. Several methods approaches have developed approach these conditions, such as fractional models derivatives. These are expected since derived using Ito’s lemma from stochastic calculus, where play a leading role. Hence, that includes basic special case expected. require computational tools advanced analytical solve associated equations. Nevertheless, it believed fractal nature processes permits economical markets problems more accurately compared conventional model. relationship between calculus fractals well-known literature. This study introduces generalized dimensions discusses its role marketing. In our analysis, we consider power-laws properties volatility, interest rated, dividend payout, which emerge several empirical regularities quantitative finance economics. We apply problem barrier values both time space. Our can used obtain many pay-off models. observe considerably affect solutions that, much smaller than unity, call increases significantly. prove powerful tool new results. Further details analyzed discussed.

Language: Английский

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Dynamical properties and new optical soliton solutions of a generalized nonlinear Schrödinger equation

The European Physical Journal Plus, Journal Year: 2023, Volume and Issue: 138(11)

Published: Nov. 30, 2023

Language: Английский

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Bifurcations, chaotic dynamics, sensitivity analysis and some novel optical solitons of the perturbed non-linear Schrödinger equation with Kerr law non-linearity

Results in Physics, Journal Year: 2023, Volume and Issue: 54, P. 107133 - 107133

Published: Nov. 1, 2023

This study introduces an analysis of bifurcations, chaotic dynamics, and sensitivity using the Galilean transformation applied to perturbed non-linear Schrödinger equation (NLSE) with Kerr-law nonlinearity. Additionally, we employ efficient Sardar sub-equation (Sse) method derive various optical soliton solutions. Initially, outline general framework Sse proposed. Next, utilize a traveling wave transform on NLSE, transforming it into system nonlinear ordinary differential equations (NLODEs) which are further separated their real imaginary components. Furthermore, apply this new solitons for NLSE Kerr law. We perform exact analytical simulations these solutions investigate effects different parameters waves.

Language: Английский

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On a Fractal–Fractional-Based Modeling for Influenza and Its Analytical Results

Qualitative Theory of Dynamical Systems, Journal Year: 2024, Volume and Issue: 23(2)

Published: Jan. 4, 2024

Language: Английский

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A novel fractal fractional mathematical model for HIV/AIDS transmission stability and sensitivity with numerical analysis

Scientific Reports, Journal Year: 2025, Volume and Issue: 15(1)

Published: March 18, 2025

Understanding the complex dynamics of HIV/AIDS transmission requires models that capture real-world progression and intervention impacts. This study introduces an innovative mathematical framework using fractal-fractional calculus to analyze dynamics, emphasizing memory effects nonlocal interactions critical disease spread. By dividing populations into four distinct compartments-susceptible individuals, infected those undergoing treatment, individuals in advanced AIDS stages-the model reflects key phases infection therapeutic interventions. Unlike conventional approaches, proposed nonlinear function, $$\frac{\nabla (\mathscr {I}+\alpha _1\mathscr {T}+\alpha _2\mathscr {A})}{\mathscr {N}}$$ , accounts for varying infectivity levels across stages (where $$\mathscr {N}$$ is total population $$\nabla$$ denotes effective contact rate), offering a nuanced view how treatment efficacy ( $$\alpha _1$$ ) _2$$ shape transmission. The analytical combines rigorous exploration with practical insights. We derive basic reproduction number {R}_0$$ assess outbreak potential employ Lyapunov theory establish global stability conditions. Using Schauder fixed-point theorem, we prove existence uniqueness solutions, while bifurcation analysis via center manifold reveals thresholds persistence or elimination. use computational scheme Adams-Bashforth method interpolation-based correction technique ensure numerical precision confirm theoretical results. Sensitivity highlights medication accessibility delaying spread as vital control strategy by identifying parameters. simulations illustrate predictive ability model, which shows order affects trajectories long-term burden. outperforms integer produces more accurate epidemiological predictions integrating memory-dependent fractional flexibility. These findings demonstrate model's value developing targeted public health initiatives, particularly environments limited resources where monitoring balancing allocation essential. In end, our work provides tool better predict manage evolving challenges bridging gap between mathematics actual control.

Language: Английский

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Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

PLoS ONE, Journal Year: 2024, Volume and Issue: 19(4), P. e0298620 - e0298620

Published: April 16, 2024

In this manuscript, we developed a nonlinear fractional order Ebola virus with novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of solution derivative is treated for system Arzel’a-Ascoli Schauder conditions. We investigate effects classical modified calculus operators, specifically Caputo operator, on behavior model. A model shows that completely continuous operator uniformly continuous, bounded according equilibrium points. reproductive number R 0 derived biological feasibility sensitivity analysis different parameters impact Sensitivity an essential tool comprehending how various affect spread illness. Through methodical manipulation important assessment their o , are able learn more about resiliency susceptibility Local stability established next Matignon method global conducted Lyapunov function feasible proposed end, numerical Newton’s polynomial through simulations compartments at orders by using real data. Our findings highlight importance operators in enhancing accuracy capturing intricate dynamics disease. This research contributes deeper understanding provides valuable insights improving disease modeling public health strategies.

Language: Английский

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