Complexity Analysis to Fractional Order Enzyme Model

Abstract

This study examines a discrete-time enzyme model with Caputo fractional order. We look into the existence and uniqueness of fixed points in the discrete dynamic model and discover parametric criteria for their local asymptotic stability. Additionally, it is demonstrated using bifurcation theory that the system experiences Period-Doubling and Neimark-Sacker bifurcation in a constrained area around the singular positive fixed point and that an invariant circle would result. It has been determined that the parameter values and the initial conditions have a significant impact on the dynamical behavior of the fractional order enzyme model. Additionally, with the use of Matlab tools, numerical analysis is offered to illustrate the theoretical debates. Therefore, numerical simulations are used to support the key theoretical findings.