Fractional order analysis of modified stretch-twist-fold flow with synchronization control

Nonlinear behavior and fractional order chaoticity with synchronization control of modified stretch-twist-fold (MSTF) flow are studied in this article. Analytical determination of the chaotification threshold is of great interest in engineering and control analysis. Generally speaking, a necessary condition of an ordinary differential system for the existence of chaos is that its spatial dimension equals at least three. However, for the fractional equation, it is not the case. It is studied that the fractional order MSTF flow exhibits rich dynamical properties and can be chaotic with the effective dimension Sigma less than 2. The chaotic behavior is conjectured on the basis of numerical simulation using the Adams-Bashforth-Moulton method. Synchronization of the fractional MSTF flow at different fractional orders is examined by an active control method. The proposed control has certain significance in terms of reducing the time and complexity for strategy implementation.