Open Access
1999 Immediate exchange of stabilities in singularly perturbed systems
N. N. Nefedov, K. R. Schneider
Differential Integral Equations 12(4): 583-599 (1999). DOI: 10.57262/die/1367267008


We study the initial value problem for singularly perturbed systems of ordinary differential equations whose associated systems have two transversally intersecting families of equilibria (transcritical bifurcation) which exchange their stabilities. By means of the method of upper and lower solutions we derive a sufficient condition for the solution of the initial value problem to exhibit an immediate exchange of stabilities. Concerning its asymptotic behavior with respect to $\varepsilon$ we prove that an immediate exchange of stabilities implies a change of the asymptotic behavior from $0(\varepsilon)$ to $0(\sqrt{\varepsilon})$ near the point of exchange of stabilities.


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N. N. Nefedov. K. R. Schneider. "Immediate exchange of stabilities in singularly perturbed systems." Differential Integral Equations 12 (4) 583 - 599, 1999.


Published: 1999
First available in Project Euclid: 29 April 2013

zbMATH: 1015.34047
MathSciNet: MR1697246
Digital Object Identifier: 10.57262/die/1367267008

Primary: 34E15
Secondary: 34C60 , 34C99 , 34D99

Rights: Copyright © 1999 Khayyam Publishing, Inc.

Vol.12 • No. 4 • 1999
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