Abstract
Chaos has important applications in physics, chemistry, biology, ecology, secure communications, cryptosystems and many scientific branches. Control and synchronization of chaotic systems are important research problems in chaos theory. Sliding mode control is an important method used to solve various problems in control systems engineering. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as insensitivity to parameter uncertainties and disturbance. In this work, we first investigate research in the dynamic analysis and properties of the enzymes-substrates reactions system with ferroelectric behaviour in the brain waves which was studied by Enjieu Kadji et al. (Chaos Solitons Fractals 32:862–882, 2007, [10]). Next, we apply multivariable super-twisting sliding mode control to globally stabilize all the trajectories of the enzymes-substrates biological chaotic system. Furthermore, we use multivariable super-twisting sliding mode control for the global chaos synchronization of identical enzymes-substrates biological chaotic systems. Super-twisting sliding mode control is very useful for the global stabilization and synchronization of the enzymes-substrates reaction system as it achieves finite time stability for the system. Numerical simulations using MATLAB are shown to illustrate all the main results derived in this work.
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Vaidyanathan, S. (2017). Super-Twisting Sliding Mode Control of the Enzymes-Substrates Biological Chaotic System. In: Vaidyanathan, S., Lien, CH. (eds) Applications of Sliding Mode Control in Science and Engineering. Studies in Computational Intelligence, vol 709. Springer, Cham. https://doi.org/10.1007/978-3-319-55598-0_19
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