Dynamics of chaotic waterwheel model with the asymmetric flow within the frame of Caputo fractional operator

Title

Dynamics of chaotic waterwheel model with the asymmetric flow within the frame of Caputo fractional operator

Creator

Deepika S.; Veeresha P.

Description

The chaotic waterwheel model is a mechanical model that exhibits chaos and is also a practical system that justifies the Lorenz system. The chaotic waterwheel model (or Malkus waterwheel model) is modified with the addition of asymmetric water inflow to the system. The hereditary property of the modified chaotic waterwheel model is analyzed to determine the system's stability and identify the parameter that contributes to the stability We also examine the factor that leads to the bifurcation. We determine the well-posed nature of the modified system. The modified chaotic waterwheel model is defined with the Caputo fractional operator. The existence and uniqueness, boundedness, stability, Lyapunov stability, and numerical simulation are studied for the modified fractional waterwheel model. The bifurcation parameter and Lyapunov exponent are examined to study the chaotic nature of the system with respect to the fractional order. The nature of the system is captured with the help of the efficient numerical approach AdamsBashforthMoulton Method. The numerical approach demonstrates that the chaotic nature of the modified chaotic waterwheel is changed into unstable nature, which could further reduce to the stable case with suitable values of the parameter. This analysis is justified with the help of Lyapunov exponent. We consider irrational order (?,e) in the present work to illustrate the reliability of fractional order. 2023 Elsevier Ltd

Source

Chaos, Solitons and Fractals, Vol-169

Date

2023-01-01

Publisher

Elsevier Ltd

Subject

AdamsBashforthMoulton method; Asymmetric flow; Caputo fractional operator; Chaotic waterwheel; Lyapunov exponent; Stability

Coverage

Deepika S., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India; Veeresha P., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India

Rights

Restricted Access

Relation

ISSN: 9600779; CODEN: CSFOE

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1016/j.chaos.2023.113298

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