Classification of functions with trivial solutions under \(t\)-equivalence


Authors

Yanqing Li - School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, P. R. China. - School of ocean information engineering, Hainan Tropical Ocean University, Sanya, Hainan 572022, P. R. China. Donghe Pei - School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, P. R. China. Dejian Huang - School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, P. R. China. - School of ocean information engineering, Hainan Tropical Ocean University, Sanya, Hainan 572022, P. R. China. Ruimei Gao - Department of Science, Changchun University of Science and Technology, Changchun, Jilin 130022, P. R. China.


Abstract

We apply singularity theory to study bifurcation problems with trivial solutions. The approach is based on a new equivalence relation called t-equivalence which preserves the trivial solutions. We obtain a sufficient condition for recognizing such bifurcation problems to be t-equivalent and discuss the properties of the bifurcation problems with trivial solutions. Under the action of t-equivalent group, we classify all bifurcation problems with trivial solutions of codimension three or less.


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ISRP Style

Yanqing Li, Donghe Pei, Dejian Huang, Ruimei Gao, Classification of functions with trivial solutions under \(t\)-equivalence, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3581--3591

AMA Style

Li Yanqing, Pei Donghe, Huang Dejian, Gao Ruimei, Classification of functions with trivial solutions under \(t\)-equivalence. J. Nonlinear Sci. Appl. (2017); 10(7):3581--3591

Chicago/Turabian Style

Li, Yanqing, Pei, Donghe, Huang, Dejian, Gao, Ruimei. "Classification of functions with trivial solutions under \(t\)-equivalence." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3581--3591


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