BIFURCATION AND CHAOS IN A DISCRETE FRACTIONAL ORDER REDUCED LORENZ MODEL WITH CAPUTO AND CONFORMABLE DERIVATIVES

This study investigates a discrete fractional order reduced Lorenz model that incorporates the Caputo and Conformable fractional derivatives respectively. The stability of equilibrium points of the model with Caputo fractional derivative are analyzed. The Conformable fractional derivative model is likewise examined. We confirm algebraically the existence and direction of Neimark-Sacker bifurcation for both models using the central manifold and bifurcation theories. The dynamic behavior of these models have been extensively investigated based on changes made to the control parameters. In addition to supporting analytical findings, numerical simulations are used to reveal chaotic characteristics such as bifurcations, phase portraits, periodic orbits, invariant closed cycles, and attractive chaotic sets. We also quantitatively compute the maximal Lyapunov exponents and fractal dimensions to validate the chaotic properties of the system. Using three different control strategies viz, OGY, hybrid control method, and state feedback method, the system's chaotic trajectory is finally stopped.