A novel 2-D chaotic enzymes-substrates reaction system and its adaptive backstepping control

Abstract

In this research work, we announce a novel 2-D chaotic enzymessubstrates reaction system and discuss its adaptive backstepping control. First, this work describes the dynamic equations and qualitative properties of the novel 2-D biological chaotic system. Our novel chaotic system is obtained by modifying the equations of the 2-D enzymes-substrates reaction systemwith ferroelectric behaviour in brain waves obtained by Kadji et al. (Chaos Solitons Fractals 32:862–882, 2001, [27]). The Maximal Lyapunov Exponent (MLE) of the novel 2-D chaotic enzymessubstrates reaction system is obtained as L1 = 0.14425. Next, this work describes the adaptive control of the novel 2-D chaotic enzymes-substrates reaction system via backstepping control method. Furthermore, this work describes the adaptive synchronization of identical novel 2-D chaotic enzymes-substrates reaction systems via backstepping control method. The main stabilization and synchronization results derived in this work are established via Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this work for the novel 2-D chaotic enzymes-substrates reaction system.