Chaos Analysis of the Fractional Genesio-Tesi System with Constant and Variable-Order Dynamics

Fractional calculus extends conventional differentiation and integration to non-integer orders, facilitating a more suitable modeling framework for complicated dynamical processes characterized by memory and long-range dependence. The fractional and variable-order fractional Genesio-Tesi systems have recently attracted significant interest owing to their rich nonlinear dynamics and the added flexibility introduced by variable fractional orders. This work comparatively studies the stability and chaotic behavior of constant-order versus variable-order formulations of the fractional Genesio–Tesi system. The study of the system dynamics is carried out by numerical simulations, including time series, bifurcation diagrams, Lyapunov exponents, and phase portraits. We identify further stability boundaries and chaotic regimes through analytical investigations based on the Jacobian eigenvalue spectrum. It is found that variable-order derivatives intensify sensitivity and transient responses, disclosing chaotic patterns that contribute to a more profound understanding of fractional nonlinear dynamics.