caa a22 4500 606167110 CHVBK 20210128100701.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10665-014-9762-x doi (NATIONALLICENCE)springer-10.1007/s10665-014-9762-x Approximation of limit cycles in two-dimensional nonlinear systems near a Hopf bifurcation by canonical transformations [Elektronische Daten] [Jianhe Shen, Huaxiong Chen, Zheyan Zhou, Shuhui Chen] A perturbation procedure is proposed that can determine the limit cycles and their associated frequencies in general two-dimensional nonlinear systems. There are three key points in the procedure - the derivation of the canonical system, a well-chosen parameter transformation, and suitable solution expansions. We show the efficiency of the perturbation method applied to a classical Rosenzweig-MacArthur predator-prey model. The explicit and analytical approximations to the limit cycles and their associated frequencies are derived. The good agreement between the analytical approximations and the numerically generated results shows the high accuracy and efficiency of the presented method, especially when the bifurcation parameter is moderately near the critical value. Springer Science+Business Media Dordrecht, 2015 Limit cycle nationallicence Perturbation procedure nationallicence Two-dimensional system nationallicence Shen Jianhe School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, People's Republic of China aut Chen Huaxiong School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, People's Republic of China aut Zhou Zheyan School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, People's Republic of China aut Chen Shuhui Department of Applied Mechanics and Engineering, Sun Yat-sen University, 510275, Guangzhou, People's Republic of China aut Journal of Engineering Mathematics Springer Netherlands 92/1(2015-06-01), 185-202 0022-0833 92:1<185 2015 92 10665 https://doi.org/10.1007/s10665-014-9762-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-014-9762-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shen Jianhe School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, People's Republic of China aut NATIONALLICENCE 700 1- Chen Huaxiong School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, People's Republic of China aut NATIONALLICENCE 700 1- Zhou Zheyan School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, People's Republic of China aut NATIONALLICENCE 700 1- Chen Shuhui Department of Applied Mechanics and Engineering, Sun Yat-sen University, 510275, Guangzhou, People's Republic of China aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 92/1(2015-06-01), 185-202 0022-0833 92:1<185 2015 92 10665