A shooting approach to layers and chaos in a forced duffing equation

[摘要] We study equilibrium solutions for the problem u(t) = epsilon(2)u(xx) -u(3) - lambdau + cos x, u(x)(0, t) = u(x)(1,t) =0 Using a shooting method we find solutions for all nonzero epsilon. For small epsilon we add to the solutions found by previous authors, especially Angenent, 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 lambda greater than or equal to lambda(0) = 3/2(2/3) and 0 < epsilon less than or equal to 1/4. We also consider the problem of bifurcation of solutions as increases. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-11-01

[关键词] Duffing equation;layer solutions;shooting methods;chaos