Canards in ?3 Export

@article{citeulike:3428863, abstract = {We give a geometric analysis of canard solutions in three-dimensional singularly perturbed systems with a folded two-dimensional critical manifold. By analysing the reduced flow we obtain singular canard solutions passing through a singularity on the fold-curve. We classify these singularities, called canard points, as folded saddles, folded nodes, and folded saddle-nodes. We prove the existence of canard solutions in the case of the folded saddle. We show the existence of canards in the folded node case provided a generic non-resonance condition is satisfied and in a subcase of the folded saddle-node. The proof is based on the blow-up method. }, author = {Szmolyan, P.}, citeulike-article-id = {3428863}, citeulike-linkout-0 = {http://dx.doi.org/10.1006/jdeq.2001.4001}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0022-0396(01)94001-X}, day = {10}, doi = {10.1006/jdeq.2001.4001}, issn = {00220396}, journal = {Journal of Differential Equations}, month = {December}, number = {2}, pages = {419--453}, posted-at = {2008-10-19 13:05:14}, priority = {3}, title = {Canards in ?3}, url = {http://dx.doi.org/10.1006/jdeq.2001.4001}, volume = {177}, year = {2001} }

TY - JOUR ID - citeulike:3428863 L3 - citeulike-article-id:3428863 N2 - We give a geometric analysis of canard solutions in three-dimensional singularly perturbed systems with a folded two-dimensional critical manifold. By analysing the reduced flow we obtain singular canard solutions passing through a singularity on the fold-curve. We classify these singularities, called canard points, as folded saddles, folded nodes, and folded saddle-nodes. We prove the existence of canard solutions in the case of the folded saddle. We show the existence of canards in the folded node case provided a generic non-resonance condition is satisfied and in a subcase of the folded saddle-node. The proof is based on the blow-up method. IS - 2 JF - Journal of Differential Equations SN - 00220396 EP - 453 TI - Canards in ?3 VL - 177 SP - 419 AU - Szmolyan, P PY - 2001/12/10/ UR - http://dx.doi.org/10.1006/jdeq.2001.4001 ER -