Study on Numerical Computation of Hard Excitation in an Autocatalytic Biochemical System

Abstract

The objective of this study is to develop, analyze, implement and compare finite-difference techniques in order to make available robust numerical approaches. An autocatalytic biochemical system in the presence of recycling enzyme is solved numerically using two numerical methods based on finite difference schemes. The first method is the well-known Euler method which is an explicit method, whereas the second method is implicit. Although the implicit method, method 2, is first order accurate in time it converges to the fixed point(s) for large time step, \(\ell\). Numerical results show the existence of hard excitation and birhythmicity.