Geodesic
Integral manifolds for slow-fast systems and the stability loss delay
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2010), pp. 93-105

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The paper is devoted to the study of the slow-fast systems under the condition that the spectrum of the linear part of the fast subsystem consists of the pair of complex conjugate eigenvalues that cross the imaginary axis from left to right. It is proved that if we introduce the additional function into the system then the modified system has the slow integral manifold with change of stability.
Keywords: integral manifolds, change of stability, stability loss delay, multiscale systems. 
@article{VSGU_2010_6_a10,
     author = {E. V. Schetinina},
     title = {Integral manifolds for slow-fast systems and the stability loss delay},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {93--105},
     publisher = {mathdoc},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2010_6_a10/}
}
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E. V. Schetinina. Integral manifolds for slow-fast systems and the stability loss delay. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2010), pp. 93-105. http://geodesic.mathdoc.fr/item/VSGU_2010_6_a10/