Dynamical Characteristics and Approximate Technique to Solve the Model of Nonlinear Biological Reactions
DOI:
https://doi.org/10.66279/ewystw03Keywords:
Michaelis–Menten Kinetics, Elzaki transform, Existence and Uniqueness, positivity, Runge–Kutta methodAbstract
In this paper, we present a rigorous mathematical analysis of the nonlinear Michaelis-Menten biochemical reaction model, formulated as a system of non-dimensional coupled nonlinear ordinary differential equations (ODEs). Using the classical theory of ordinary differential equations, comparison principles, and Lyapunov's direct method, fundamental qualitative properties of the model, such as existence, uniqueness, non-negativity, boundedness, and local and global asymptotic stability of solutions, are established. The Elzaki Transform Homotopy Perturbation Method (ETHPM) is used to obtain an accurate approximate analytical solution, and its accuracy is studied by direct comparison with the fourth-order Runge-Kutta (RK4) method and error analysis. Numerical simulations confirm the temporal dynamics of biochemical systems and validate the efficiency and accuracy of the proposed semi-analytical approach. The results indicate that the Elzaki transform decomposition framework provides a computationally efficient, linearization-free, and highly accurate tool for analyzing nonlinear biochemical reaction models with wider applicability to a broad class of nonlinear problems arising in mathematical biology and applied science.
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