Investigation of chaotic behavior in a Lorenz-like system with fractional derivatives

Abstract

In recent years, fractional-order dynamical systems have attracted significant attention because of their ability to describe memory effects and hereditary properties found in many physical and engineering processes. Fractional calculus extends the concept of differentiation and integration to non-integer orders, providing a more flexible mathematical framework for modeling and analyzing complex system behaviors. Within this framework, the study of chaotic dynamics in fractional-order systems has become an active research area since many well-known chaotic models show new and qualitatively different behaviors when generalized to fractional derivatives. This study revisits a classical chaotic system originally defined in the integer-order setting and analyzes its behavior using fractional-order calculus. The main objective is to examine how fractional differentiation influences the system’s chaotic dynamics and sensitivity to initial conditions. To achieve this, numerical simulations are performed to demonstrate the effects of different fractional orders on the development and evolution of chaotic behavior.

Keywords

fractional-order chaotic systems / nonlinear dynamics / memory effects / numerical simulation

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