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Conditions are then given to ensure that a globally attractive limit cycle in the zero dynamics results in a globally attractive limit cycle in the whole system.
a ( μ = 2 ): system (1a)–(1c) admits an attractive limit cycle of relaxation type.
A method for the generation of globally attractive limit cycles for nonlinear systems is presented.
This singular point is unstable and the system displays a globally attractive limit cycle of relaxation type.
Let us recall that the transition between the excitable state and the oscillatory regime that occurs in a very narrow interval of Ca values is the well-known canard phenomenon, leading to the existence of small attractive limit cycle following the middle branch of the cubic for a while [20].
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That suggests the carry-trade (selling borrowed yen to invest elsewhere) will remain attractive, limiting the yen's rise.The doomsday scenarioFor true dollar pessimists, these cyclical considerations are only part of the story.
b ( μ = 2.4 ): system (1a)–(1c) admits an attractive MMO limit cycle.
This type of orbit is obtained for small values of μ. b Attractive MMO limit cycle with small oscillations near the fold F −.
In the case of panel (b), system (1a)–(1c) admits an attractive MMO limit cycle and the small oscillations reproduce the quiescent phase of the calcium pattern at the baseline level between two successive peaks.
Supposing that the oscillating species are x, the non-oscillating species are y, and ∈ is a small parameter, then we have: (30) ϵ d x d t = f (x, y ) (31) d y d t = g (x, y ) It is supposed that for any y, the fast dynamics (30) has an attractive hyperbolic limit cycle x = ψ (τ, y), of period T y): ψ (τ + T y), y) = ψ τ, y) (τ = t/ ϵ).
Remediation limited to the identification and support of those already demonstrating incompetent skills, or dangerous attitudes may be attractive by limiting the numbers generated.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com