Chemical Oscillations:
The Templator Model

Introduction

The Template model is a simplified version of the Rebek's experiments on self-replicating molecules.  Also it has been modified to study DNA replications via a triple stranded complex.  The simplified version due to Peacock-Lopez is discussed in the Chemical Educator.

Linear Stability Analysis
of the
Templator Model
MATHEMATICA Ver. 4.0

Template mechanism

Steady states

Jacobian or relaxation matrix

Minimal Template, ku = 0.

Steady States

Trace's zeros

Discriminat's zeros

Templator model

Steady states

Second order approximation

From our analytic study of the Templator

Brute Force Calculation of the trace's zeros

Comparison betwwen brute force and other methods

Some other figures for the Templator

Time series

ODE's

First we define the differential equations

[Graphics:Images/templator_gr_129.gif]

Second we define the substitution to use NDSolve

[Graphics:Images/templator_gr_130.gif]

Define the parameter values used inthe integration.  Also we Plot the solutions

Trajectories

Final figures


Converted by Mathematica      November 14, 2000