CHAOTIC DYNAMICS OF THE FRACTIONAL ORDER SCHNAKENBERG MODEL AND ITS CONTROL

The Schnakenberg model is thought to be the Caputo fractional derivative. A discretization process is first used to create caputo fractional differential equations for the Schnakenberg model. The fixed points in the model are categorized topologically. Then, we show analytically that a fractional order Schnakenberg model supports a Neimark-Sacker (NS) bifurcation and a Flip-bifurcation under certain parametric conditions. Using central manifold and bifurcation theory, we demonstrate the presence and direction of NS and Flip bifurcations. The parameter values and the initial conditions have been found to profoundly impact the dynamical behavior of the fractional order Schnakenberg model. Numerical simulations demonstrate chaotic behaviors like bifurcations, phase portraits, period 2, 4, 7, 8, 10, 16, 20 and 40 orbits, invariant closed cycles, and attractive chaotic sets in addition to validating analytical conclusions. To support the system's chaotic characteristics, we also quantitatively compute the maximal Lyapunov exponents and fractal dimensions. Finally, the chaotic trajectory of the system is stopped using the OGY approach, hybrid control method, and state feedback method.