MATHEMATICAL MODEL FOR ENZYME: STABILITY ANALYSIS CHAOS DIGNOSIS AND CONTROL
Maha W. khaleel College of Computer Science and Mathematics, Mosul University, Mosul, Iraq.
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Abstract Enzyme kinetics mathematically is important since it helps us understand how enzymes work and analyzed interactions with in cells making them essential in medicine, industry and scientific research. We suggest a three-dimensional biomathematical autonomous system, which is made up of three ordinary differential equations, that represent the interaction of the model variables N, S, R, where N is the excited enzyme, R is the unexcited enzyme and S is the number of substrate molecules. Real data for sick people was taken from the (Biostudies/Array-Express) website, and the parameters of the suggested system for lipase enzyme kinetics were estimated. The dynamic properties of the suggested system are verified by equilibrium points and it’s stability such as roots of characteristic equation, Routh array, Hurwitz stability criteria and Lyapunov function, dissipativity, Hopf bifurcation and Lyapunov dimension based on Lyapunov exponents L_1=0.182739, L_2=0.229701 and L_3=-2.612439 . the results of the analysis showed that lipase enzyme kinetics system is unstable and highly chaotic, chaos was efficiently controlled using adaptive control and active control techniques.
Keywords
Adaptive and Active Control, Chaos, Enzyme Kinetics Model, Hopf Bifurcation, Stability Analysis, |