To do the linear stability analysis for all the fixed points of the equation d ϕ dt = f( ϕ ) , where f( ϕ ) = - sin ϕ + γ sin ϕ cos ϕ = sin ϕ (γ cos ϕ - 1) . Concept Introduction: Fixed points come off when f( ϕ ) = 0 . If f ' ( ϕ * ) > 0 , then ϕ * is an unstable fixed point If f ' ( ϕ * ) < 0 , then ϕ * is a stable fixed point.

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Chapter 3.5, Problem 2E

Interpretation Introduction

Interpretation:

To do the linear stability analysis for all the fixed points of the equation dϕdt = f(ϕ), where f(ϕ) = - sin ϕ + γsinϕ cos ϕ = sin ϕ (γ cos ϕ - 1).

Concept Introduction:

Fixed points come off when f(ϕ) = 0.

If f'(ϕ) > 0, then ϕ is an unstable fixed point

If f'(ϕ) < 0, then ϕ is a stable fixed point.

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