A shooting approach to layers and chaos for a forced Duffing equation
| dc.creator | Ai, SB. | |
| dc.creator | Hastings, S. | |
| dc.date | 2001-05-05 | |
| dc.date.accessioned | 2026-07-07T04:41:37Z | |
| dc.date.available | 2026-07-07T04:41:37Z | |
| dc.description | We study equilibrium solutions for the problem $u_t=ε^2 u_{xx} -u^3 +λu -cos(t)$,$u_x(0,t)=u_x(L,t)=0$. Using a shooting method we find solutions for all non-zero $ε.$ For small $ε$ we add to the solutions found by previous authors, especially Angennent, Mallet-Paret and Peletier, and Hale and Sakamoto, and also give new elementary ode proofs of their results. Among the new results is the existence of internal layer-type solutions. Considering the ode satisfied by equilibria, but on an infinite interval, we obtain chaos results for $λ\geq λ_{0}=\frac{3}{2^{2/3}}$ and $0<ε\leq {1/4}.$ We also consider the problem of bifurcation of solutions as $λ$ increases from $0.$ | |
| dc.identifier | https://arxiv.org/abs/math/0105043 | |
| dc.identifier | http://arxiv.org/abs/math/0105043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61431 | |
| dc.subject | Dynamical Systems | |
| dc.title | A shooting approach to layers and chaos for a forced Duffing equation | |
| dc.type | text |