Efficient Numerical Techniques for Investigating Chaotic Behavior in the Fractional-Order Inverted Rössler System

Symmetry, Journal Year: 2025, Volume and Issue: 17(3), P. 451 - 451

Published: March 18, 2025

In this study, the numerical scheme for Caputo fractional derivative (NCFD) method and He–Laplace (H-LM) are two powerful methods used analyzing fractional-order systems. These approaches in study of complex dynamics inverted Rössler system, particularly detection chaotic behavior. The enhanced NCFD is reliable accurate simulations by capturing intricate Further, analytical solutions obtained using H-LM system. This popular due to its simplicity, stability, ability handle most initial values, yielding very results. Combining insights from with robust accuracy approach yields a comprehensive understanding system’s dynamics. advantages include high capture offers simplicity stability. proposed prove be capable detecting attractors, estimating their behavior correctly, finding solutions. findings confirm that NCFD- H-LM-based promising modeling solution Since these results provide improved broad class models, they will thus greatest use forthcoming applications engineering science.

Language: Английский

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Variable-Fractional-Order Nosé–Hoover System: Chaotic Dynamics and Numerical Simulations

Fractal and Fractional, Journal Year: 2025, Volume and Issue: 9(5), P. 277 - 277

Published: April 25, 2025

This study explores the variable-order fractional Nosé–Hoover system, investigating evolution of its chaotic and stable states under derivatives. Variable-order derivatives introduce greater complexity adaptability into a system’s dynamics. The main objective is to examine these effects through numerical simulations, showcasing how changes in order function influence behavior. behavior shown by phase space orbits time series for various variable orders α. We look at system acts using solutions simulations. different α show effects. findings emphasize role enhancing behavior, offering novel insights their impact on dynamical systems.

Language: Английский

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Optimal control and stability analysis of influenza transmission dynamics with quarantine interventions

Modeling Earth Systems and Environment, Journal Year: 2025, Volume and Issue: 11(4)

Published: April 28, 2025

Language: Английский

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On Extended Numerical Discretization Technique of Fractional Models with Caputo-Type Derivatives

Fractal and Fractional, Journal Year: 2025, Volume and Issue: 9(5), P. 289 - 289

Published: April 28, 2025

In this work, we investigate the extended numerical discretization technique for solution of fractional Bernoulli equations and SIRD epidemic models under Caputo fractional, which is accurate versatile. We have demonstrated method’s strength in examining complex systems; it found that method produces solutions are identical to exact approximate series solutions. The ENDT its ability proficiently handle systems governed by differential while preserving memory hereditary characteristics. Its simplicity, accuracy, flexibility render an effective instrument replicating real-world phenomena physics biology. offers stability, efficiency compared traditional methods. It effectively handles challenges systems, supports any order, simple implement, improves computing with sophisticated methodologies, applies predictions biological simulations.

Language: Английский

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Novel Dynamic Behaviors in Fractional Chaotic Systems: Numerical Simulations with Caputo Derivatives

Axioms, Journal Year: 2024, Volume and Issue: 13(11), P. 791 - 791

Published: Nov. 16, 2024

Over the last several years, there has been a considerable improvement in possible methods for solving fractional-order chaotic systems; however, achieving high accuracy remains challenge. This work proposes new precise numerical technique systems. Through simulations, we obtain types of complex and previously undiscussed dynamic behaviors.These phenomena, not recognized prior results or theoretical estimations, underscore unique dynamics present fractional We also study effects parameters β1, β2, β3 on system’s behavior, comparing them to integer-order derivatives. It demonstrated via findings that suggested is consistent with conventional systems while simultaneously providing an even higher level precision. demonstrate efficacy precision this through which demonstrates method useful investigation complicated models.

Language: Английский

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Optimal control and analysis of a stochastic SEIR epidemic model with nonlinear incidence and treatment

AIMS Mathematics, Journal Year: 2024, Volume and Issue: 9(12), P. 33532 - 33550

Published: Jan. 1, 2024

<p>In this paper, we represented the optimal control and dynamics of a stochastic SEIR epidemic model with nonlinear incidence treatment rate. By using Lyapunov function method, existence uniqueness global positive solution were proved. The dynamic analysis was studied found that has an ergodic stationary distribution when $ R_{0}^{s} &gt; 1 $. disease extinct R_{0}^{e} &lt; obtained by theory. numerical simulation our conclusion carried out. results showed decreased increase variables.</p>

Language: Английский

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