| Full text | |
| Author(s): |
Candido, Murilo R.
;
Llibre, Jaume
;
Novaes, Douglas D.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Nonlinearity; v. 30, n. 9, p. 3560-3586, SEP 2017. |
| Web of Science Citations: | 6 |
| Abstract | |
In this work we first provide sufficient conditions to assure the persistence of some zeros of functions having the form g(z, epsilon) - g(0) (z) + Sigma(k)(i-1) epsilon(i) g(i) (z) + O (epsilon(k+1)), for | epsilon | not equal 0 sufficiently small. Here g(i) : D -> R-n, for i = 0, 1,..., k, are smooth functions being D subset of R-n an open bounded set. Then we use this result to compute the bifurcation functions which allow us to study the periodic solutions of the following T-periodic smooth differential system x' = F-0 (t, x) + Sigma(k)(i=1) epsilon(i) F-i (t, x) + O (epsilon(k+1)), (t, z) is an element of S-1 x D. It is assumed that the unperturbed differential system has a sub-manifold of periodic solutions Z, dim(Z) <= n. We also study the case when the bifurcation functions have a continuum of zeros. Finally we provide the explicit expressions of the bifurcation functions up to order 5. (AU) | |
| FAPESP's process: | 16/11471-2 - Sliding motion in discontinuous dynamical systems: periodic solutions, homoclinic connections, and nonlinear sliding modes |
| Grantee: | Douglas Duarte Novaes |
| Support Opportunities: | Regular Research Grants |