A computational approach for the generalised GenesioTesi systems using a novel fractional operator

Title

A computational approach for the generalised GenesioTesi systems using a novel fractional operator

Creator

Deepika S.; Ranganathan H.B.; Veeresha P.

Description

This article presents the novel fractional-order GenesioTesi system, along with discussions of its boundedness, stability of the equilibrium points, Lyapunov stability, uniqueness of the solution and bifurcation. The efficient predictorcorrector approach is employed to quantitatively analyse the GenesioTesi system in fractional order. The findings enable conceptualisation and visualisation of the presented novel fractional-order GenesioTesi systems. The modified systems are proposed for future study on chaos control and applying the same for secure communication. Bifurcation analysis is carried out to see the variation in the systems behaviour from stability to chaos. The results of the bifurcation analysis support the results obtained for the stability of the equilibrium points. The system behaves chaotically since all the equilibrium points are unstable. The findings demonstrate a torus attractor for some of the suggested systems and a chaotic attractor for some of the novel fractional-order GenesioTesi systems. The systems torus attractor changes into a steady state when the order is reduced from integer to fractional. Changing the parameter values for one of the modified systems also shifts the systems behaviour, with the point attractor replacing the torus attractor. The point attractor of one of the systems changes into a steady character when the systems order is reduced from integer to fractional. The behaviour for one modified system is the same for fractional and integer orders. This discovery paves the way for the future study of the modified GenesioTesi system. This article gives a new direction to utilise these proposed GenesioTesi systems and study them extensively. The chaotic behaviour of the modified system can be used for secure communication. The synchronisation and chaos control of the modified system is recommended. 2024, Indian Academy of Sciences.

Source

Pramana - Journal of Physics, Vol-98, No. 1

Date

2024-01-01

Publisher

Springer

Subject

02.30.Hq; 02.60.Cb; 98.80.Cq; caputo fractional derivative; fractional order; GenesioTesi system; lyapunov stability; numerical method

Coverage

Deepika S., Centre for Mathematical Needs, Department of Mathematics, Christ (Deemed to be University), Bengaluru, 560029, India; Ranganathan H.B., Centre for Mathematical Needs, Department of Mathematics, Christ (Deemed to be University), Bengaluru, 560029, India; Veeresha P., Centre for Mathematical Needs, Department of Mathematics, Christ (Deemed to be University), Bengaluru, 560029, India

Rights

Restricted Access

Relation

ISSN: 3044289; CODEN: PRAMC

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1007/s12043-023-02706-x

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