A shooting approach to layers and chaos for a forced Duffing equation

SB. Ai, S. Hastings

We study equilibrium solutions for the problem $u_t={\epsilon }^2{u}_{xx}-u^3+\lambda u-cos(t)$,$u_x(0,t)=u_x(L,t)=0$. Using a shooting method we find solutions for all non-zero $\epsilon .$ For small $ε…