Dynamic analysis and SDRE control applied in a mutating autocatalyst with chaotic behavior

In this work, an autocatalytic chemical reactions model with mutation is investigated, and a nonlinear control is proposed to lead the system to a behavior that maintains the system with a desired behavior and with suppress the chaotic behavior. Numerical results considering a broad analysis of the system parameters confirmed the chaotic behavior using phase portraits, bifurcation diagrams and Lyapunov exponents. An analysis of the system behavior in fractional order considering the Atangana–Baleanu–Caputo operator was performed to include the memory effect in the system dynamics. The numerical results obtained demonstrated that the system is extremely sensitive to variations in the order of the derivative, taking the system from chaotic behavior to periodic behavior with small variations in the order of the derivative. The chaotic behavior of the system is proven in fractional order by the 0–1 test and a scale index based on the wavelets test. The proposed control demonstrated to be efficient in maintaining the main product (ethanol) output concentration at the desired level.