Adaptive synchronization of fractional-order quadratic chaotic flows with nonhyperbolic equilibrium

This paper considers a fractional-order quadratic chaotic flow with nonhyperbolic equilibrium in a class of three-dimensional autonomous differential equations. Afterward, a design technique of adaptive sliding mode disturbance-observer for synchronization of fractional-order quadratic chaotic flows with nonhyperbolic equilibriums and time-varying disturbances is offered. Applying the Lyapunov stability concept, the recommended control method satisfies that the states of the fractional-order master and slave quadratic chaotic systems are synchronized quickly. Whereas the upper bounds of disturbances are unknown, an adaptive regulation scheme is advised to estimate them. In the following, the proposed disturbance-observer realizes disturbance approximation error. Finally, simulation results are presented in three different examples to exhibit the effectiveness of the offered method on the fractional-order quadratic chaotic systems in the presence of external disturbances.