Chapter 3.7, Problem 5E

Interpretation Introduction

Interpretation:

Determine the dimensionless form of the given system. For s = 0 and $r<r_c$, there are two fixed points and determine value of $r_c$. Analyze the system for $\text{g(0) = 0}$ and $\text{s}$ is slowly increased from zero and again goes back to zero. Find the parametric equations for the bifurcation curves in (r, s) plane and classify bifurcation. Using the computer plot the stability diagram in (r, s) plane

Concept Introduction:

Dimensionless Formulation: The advantage of making the equation dimensionless is

The number of parameters in the equation reduces due to lumping them together into dimensionless groups

Dimensionless formulation gives the definition of parameter how much small it is $(\ll 1)$

To find the parametric equations, differentiate the dimensionless system equation.

To summarize the result, the stability diagram is plotted using parametric equations of r and s.