Computing Hopf Bifurcations. II: Three Examples From Neurophysiology Export

@article{citeulike:6107432, abstract = {In a previous paper we presented algorithms for detecting Hopf bifurcations in two-parameter families of vector elds based on classical algebraic constructions. In addition to their utility as augmented systems for use with standard Newton-type continuation methods, they were shown to be particularly well-adapted for solution by computer algebra techniques for vector fields of small or moderate dimension. The present study examines the performance of these methods on test problems selected from models of current research interest in neurophysiology. Implementation issues are examined and the numerical properties of the proposed methods are compared with several alternative algorithms for Hopf pathfollowing that appear in the literature.}, author = {Guckenheimer, John and Myers, Mark}, citeulike-article-id = {6107432}, citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJOCE3000017000006001275000001&idtype=cvips&gifs=yes}, citeulike-linkout-1 = {http://link.aip.org/link/?SCE/17/1275}, journal = {SIAM Journal on Scientific Computing}, keywords = {bifurcation, hopf, routh-hurwitz}, number = {6}, pages = {1275--1301}, posted-at = {2009-11-13 05:14:37}, priority = {2}, publisher = {SIAM}, title = {Computing Hopf Bifurcations. II: Three Examples From Neurophysiology}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJOCE3000017000006001275000001&idtype=cvips&gifs=yes}, volume = {17}, year = {1996} }

TY - JOUR ID - citeulike:6107432 L3 - citeulike-article-id:6107432 N2 - In a previous paper we presented algorithms for detecting Hopf bifurcations in two-parameter families of vector elds based on classical algebraic constructions. In addition to their utility as augmented systems for use with standard Newton-type continuation methods, they were shown to be particularly well-adapted for solution by computer algebra techniques for vector fields of small or moderate dimension. The present study examines the performance of these methods on test problems selected from models of current research interest in neurophysiology. Implementation issues are examined and the numerical properties of the proposed methods are compared with several alternative algorithms for Hopf pathfollowing that appear in the literature. IS - 6 JF - SIAM Journal on Scientific Computing EP - 1301 TI - Computing Hopf Bifurcations. II: Three Examples From Neurophysiology PB - SIAM VL - 17 SP - 1275 KW - bifurcation KW - hopf KW - routh-hurwitz AU - Guckenheimer, John AU - Myers, Mark PY - 1996/// UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJOCE3000017000006001275000001&idtype=cvips&gifs=yes ER -