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According to the geometric singular perturbation theory, the dynamical behavior of the two timescale systems is governed by the structure of the slow manifold including the shape, stability, and bifurcation of the slow manifold, as well as the location and stability of the equilibrium of the two timescale systems.
A non-trivial definition of the stabilization objective is proposed and the two timescale behavior of the SAF is exploited to apply the Averaging technique and Input to State Stability arguments in the control design.
With the rambling-trembling hypothesis, Zatsiorsky and Duarte [ 80] put forward an alternative method which also differentiates between two timescale components in the COP signal.
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The two timescales, however, are rather different, as is the dramatic thrust of each part.
The above transition is the result of a competition between two timescales.
The results demonstrate three typical failure modes induced by the competition of two timescales involved.
We identify under-recording of Volcanic Explosivity Index (VEI) 4 5 eruptions on two timescales.
The difference between the two timescales gets smaller as the dust grains become larger.
4, which features three distinct timescales during the silent phase and, due to the larger size of d, two timescales during the active phase.
Unlike the MB solution in [13 15], our analysis shows that SB solution features are lost under the natural groupings to two timescales, supporting the preliminary conclusion that SB dynamics in system (1a)–(1g) requires at least three timescales.
The difference in GEC responses to EUV variations on the two timescales is consistent with that in thermospheric responses.
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