A system obeys with control parameter .

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Nonlinear dynamics and chaos · Nonlinear dynamics and chaos

Many Parts, One Behaviour, Ch Pattern formation: instabilities that choose a wavelength

Problem

A system obeys

\dot x = rx - 3x^3

with control parameter

r = 0.6

. ((a)) Find all fixed points

x^*

. ((b)) Determine the stability of each fixed point from the sign of

f'(x^*)

, where

f(x) = rx-3x^3