Asymptotic expansions for a family of non-generic canards using parametric representation

作者: Bo-Wei Qin , Kwok-Wai Chung , Antonio Algaba , Alejandro J. Rodríguez-Luis

DOI: 10.1016/J.AML.2020.106355

关键词:

摘要: Abstract Asymptotic expansions are of great interest and significance in the study canard explosions singularly perturbed systems. Several classical methods have been developed to compute such expansions. However, for non-generic case considered this letter, those fail do so. There only exists an estimation on first non-zero term literature. Our aim is propose a new approach find asymptotic iteratively. Moreover, exact value provided terms Airy function. The numerical results validate our analytical approximations.

参考文章(17)
E. Benoît, Chasse au canard Universite Louis Pasteur, Département de Mathématique, Institut de Recherche Mathematique Avancee, Laboratoire Associé au C. N. R. S. no. 1. ,(1980)
Mathieu Desroches, John Guckenheimer, Bernd Krauskopf, Christian Kuehn, Hinke M. Osinga, Martin Wechselberger, Mixed-Mode Oscillations with Multiple Time Scales Siam Review. ,vol. 54, pp. 211- 288 ,(2012) , 10.1137/100791233
G.N. Gorelov, V.A. Sobolev, Duck-trajectories in a thermal explosion problem Applied Mathematics Letters. ,vol. 5, pp. 3- 6 ,(1992) , 10.1016/0893-9659(92)90002-Q
Feng Xie, Maoan Han, Existence of canards under non-generic conditions Chinese Annals of Mathematics, Series B. ,vol. 30, pp. 239- 250 ,(2009) , 10.1007/S11401-008-0225-4
A K Zvonkin, M A Shubin, Non-standard analysis and singular perturbations of ordinary differential equations Russian Mathematical Surveys. ,vol. 39, pp. 69- 131 ,(1984) , 10.1070/RM1984V039N02ABEH003091
Francesco Marino, Gustau Catalán, Pedro Sánchez, Salvador Balle, Oreste Piro, Thermo-Optical "Canard Orbits" and Excitable Limit Cycles Physical Review Letters. ,vol. 92, pp. 073901- ,(2004) , 10.1103/PHYSREVLETT.92.073901
E. Freire, E. Gamero, A.J. Rodríguez-Luis, First-order approximation for canard periodic orbits in a van der Pol electronic oscillator Applied Mathematics Letters. ,vol. 12, pp. 73- 78 ,(1999) , 10.1016/S0893-9659(98)00152-9
M. Krupa, P. Szmolyan, Relaxation Oscillation and Canard Explosion Journal of Differential Equations. ,vol. 174, pp. 312- 368 ,(2001) , 10.1006/JDEQ.2000.3929
J. Rankin, M. Desroches, B. Krauskopf, M. Lowenberg, Canard cycles in aircraft ground dynamics Nonlinear Dynamics. ,vol. 66, pp. 681- 688 ,(2011) , 10.1007/S11071-010-9940-Y