Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 3.7, Problem 7E
Interpretation Introduction

Interpretation:

To sketch the graph of the nonlinear function g(p) = βpnKn+pn, for n >> 1 and to find the simple shape the function approaches as n, if the basal expression is given as p˙ = α +βpnKn+pn - δp. The phase portrait for the system for δK - α > β, δK - α = β2, and δK - α < 0 is to be plotted. To plot the bifurcation diagram for the system, assuming δK > β, and to indicate how the location and stability of the fixed points p* vary with respect to α. To discuss how p behaves if is very slowly

increased from α = 0 to α > δK, and then very slowlydecreased back to α = 0. To show that such a pulsed stimulation leads to hysteresis.

Concept Introduction:

The basal expression is

p˙ = α +βpnKn+pn - δp

Here α is the basal transcription rate, β is the maximal transcription rate, K is the activation coefficient, and δ is the decay rate of the protein.

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