A chaos control strategy for the fractional 3D LotkaVolterra like attractor

Title

A chaos control strategy for the fractional 3D LotkaVolterra like attractor

Creator

Naik M.K.; Baishya C.; Veeresha P.

Description

In this paper, we have considered a three-dimensional LotkaVolterra attractor in the frame of the Caputo fractional derivative to examine its dynamics. The theoretical concepts like existence and uniqueness and boundedness of the solution are analyzed. To regulate the chaos in this fractional-order system, we have developed a sliding mode controller and conditions for global stability of the controlled system with and without uncertainties and outside disruptions are derived. The ability of the designed controller is examined in terms of both commensurate and non-commensurate fractional order derivatives for all the aspects. The Lyapunov exponent is the novelty of this paper which is used to illustrate the behavior of the chaos and demonstrate the dissipativeness of the considered chaotic system. We have examined the effect of fractional order derivatives in this system. With the help of numerical simulations, the theoretical claims regarding the impact of the controller on the system are established. 2023 International Association for Mathematics and Computers in Simulation (IMACS)

Source

Mathematics and Computers in Simulation, Vol-211, pp. 1-22.

Date

2023-01-01

Publisher

Elsevier B.V.

Subject

Caputo fractional derivative; Chaos; LotkaVolterra like attractor; Predictorcorrector method; Sliding mode control

Coverage

Naik M.K., Department of Studies and Research in Mathematics, Tumkur University, Tumkur, 572103, India; Baishya C., Department of Studies and Research in Mathematics, Tumkur University, Tumkur, 572103, India; Veeresha P., Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India

Rights

Restricted Access

Relation

ISSN: 3784754; CODEN: MCSID

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1016/j.matcom.2023.04.001

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