Canard Phenomena in Oscillations of a Surface Oxidation Reaction

AbstractIn this paper we investigate canard phenomena occurring in oscillations of a surface oxidation reaction which can be modeled by a three-dimensional singularly perturbed system of ordinary differential equations with two fast variables. By using asymptotic methods, we prove the existence of the maximal canard of the mentioned model, and provide sufficient conditions for the existence of stable canard cycles.

[1]  Neil Fenichel.  Geometric singular perturbation theory for ordinary differential equations , 1979 .

[2]  Jeff Moehlis,et al.  Canards in a Surface Oxidation Reaction , 2002, J. Nonlinear Sci..

[3]  Katharina Krischer,et al.  Oscillatory CO oxidation on Pt(110) : modeling of temporal self-organization , 1992 .

[4]  Christopher Jones,et al.  Geometric singular perturbation theory , 1995 .

[5]  V. Sobolev,et al.  Integral manifolds, canards and black swans , 2001 .

[6]  A. Y. Kolesov,et al.  Asymptotic Methods in Singularly Perturbed Systems , 1994 .

[7]  Freddy Dumortier,et al.  Canard Cycles and Center Manifolds , 1996 .

[8]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[9]  P. Szmolyan,et al.  Canards in R3 , 2001 .

[10]  Peter Szmolyan,et al.  Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points - Fold and Canard Points in Two Dimensions , 2001, SIAM J. Math. Anal..

[11]  M. Krupa,et al.  Relaxation Oscillation and Canard Explosion , 2001 .

[12]  É. Benoît.  Chasse au canard , 1980 .

[13]  K. Bar-Eli,et al.  Canard explosion and excitation in a model of the Belousov-Zhabotinskii reaction , 1991 .

[14]  Wiktor Eckhaus,et al.  Relaxation oscillations including a standard chase on French ducks , 1983 .

[15]  P. Holmes,et al.  CO oxidation on thin Pt crystals: Temperature slaving and the derivation of lumped models , 2003 .

[16]  Ping Bi,et al.  Bifurcation of limit cycles and separatrix loops in singular Lienard systems , 2004 .

[17]  J. Callot,et al.  Chasse au canard , 1977 .

[18]  G. Chumakov,et al.  Relaxation oscillations in a kinetic model of catalytic hydrogen oxidation involving a chase on canards , 2003 .