Chapter 8.5, Problem 1E

Interpretation Introduction

Interpretation:

To show that ${\left(\text{ln}\left({\text{I - I}}_{\text{c}}\right)\right)}^{-1}$ has infinite derivatives of all orders at ${\text{I}}_{\text{c}}$ and try to derive a formula for ${\text{f}}^{\left(\text{n+1}\right)}\left(\text{I}\right)$ in terms of ${\text{f}}^{\left(\text{n}\right)}\left(\text{I}\right)$, where ${\text{f}}^{\left(\text{n}\right)}\left(\text{I}\right)$ denotes the $\text{n th}$ derivative of $\text{f}\left(\text{I}\right)$.

Concept Introduction:

$\text{I}$ is the dimensionless damping and applied current. ${\text{I}}_{\text{c}}$ is the critical current.

If $\text{I}$ is brought back down, the limit cycle persists below $\text{I=1}$ but its frequency tends to zero continuously as ${\text{I}}_{\text{c}}$ is approached.