NDLI: Quasi-static transient and mixed mode oscillations induced by fractional derivatives effect on the slow flow near folded singularity

Content Provider	Springer Nature Link
Author	Ngueuteu, G. S. M. Yamapi, R. Woafo, P.
Copyright Year	2014
Abstract	This paper aims at offering an insight into the dynamical behaviors of incommensurate fractional-order singularly perturbed van der Pol oscillators subjected to constant forcing, especially when the forcing is close to Andronov–Hopf bifurcation points. These bifurcation points are predicted thanks to the theorem on stability of incommensurate fractional-order systems, as functions of the forcing and fractional derivative orders. When the forcing is chosen near Andronov–Hopf bifurcation, the dynamics of fractional-order systems show a static-looking transient regime whose length increases exponentially with the closeness to the bifurcation point. This peculiar phenomenon is not common in numerical simulation of dynamical systems. We show that this quasi-static transient behavior is due to the combine action of the slow passage effect at folded saddle-node singularity and fractional derivation memory effect on the slow flow around this singularity; this forces the system to remain for a long time in the vicinity of its equilibrium point, though unstable. The system frees oneself from this quasi-static transient state by spiraling before entering relaxation oscillation. Such a situation results in mixed mode oscillations in the oscillatory regime. One obtains mixed mode oscillations from a very simple system: A two-variable system subjected to constant forcing.
Starting Page	2717
Ending Page	2729
Page Count	13
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	78
Issue Number	4
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-08-20
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Singular perturbation theory Fractional-order derivation Folded saddle-node singularity Canards Mixed mode oscillations Quasi-static transient Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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