Harnessing Adaptive Synchronization in Enzyme-Substrate Systems with Brain Wave-Like Ferroelectric Behavior

Abstract: This paper explores the application of chaos in various physical, electrical, chemical, and biological systems, with a specific focus on enzymes-substrate reactions exhibiting ferroelectric behaviour in brain waves. The study conducted by Enjieu Kadji, Chabi Orou, Yamapi, and Woafo (2007) is investi- gated, which examines the dynamic analysis and global chaos synchronization of a 2-D non-autonomous enzymes-substrates system subjected to a cosinusoidal forcing term. The phase portraits of the chaotic behaviousr in the enzymes-substrates system are depicted. Furthermore, novel adaptive control techniques are developed to achieve global synchronization of identical enzyme-substrates systems with uncertain parameters. The main results for global synchronization are derived using backstepping control, and MATLAB plots are included to illustrate these findings.