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

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 Adams–Bashforth–Moulton 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 (π , e) in the present work to illustrate the reliability of fractional order. • We analyzed the mathematical model of the chaotic water wheel model (or Malkus water wheel model) and modified with the addition of the asymmetric water inflow to the system. • The existence and uniqueness, boundedness, and Lyapunov stability are presented. • The efficient numerical method is applied to the system to demonstrate its nature. • The complexity of the obtained numerical results is illustrated with all the possible cases. [ABSTRACT FROM AUTHOR]