Chapter 2.4, Problem 3E

Interpretation Introduction

Interpretation:

By using linear stability analysis, fixed points of the $\dot{\text{x}}\text{ = tan x}$ are to be determined. If the linear stability analysis fails to find the fixed points of the system, use a graphical argument to decide the stability.

Concept Introduction:

Determine the fixed point for the equation $\dot{\text{x}}\text{ = tan x}$. The condition for a fixed point is $\dot{\text{x}}\text{=0}$

If ${{\text{f}}^{\prime }\text{ (x}}^{\text{*}}\text{) < 0}$, fixed points will be stable.

If , fixed points will be unstable.