4: Elucidating chaos in dynamical systems via fractional calculus
Abstract
This chapter focuses on understanding chaos in dynamical systems by employing fractional calculus. The dynamics of fractional-order chaotic systems are explored, with a specific examination of chaos in commensurate-order fractional systems and incommensurate-order fractional systems. The chapter then delves into the practical applications of chaos indicators in fractional dynamics systems, discussing various tools available for detecting chaos and their effectiveness. The model formulation is presented, followed by an analysis of the equilibrium points and the proof of the existence and uniqueness of solutions for the system. Numerical approaches using the Caputo–Fabrizio ...
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