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Multimodal oscillations in systems with strong contraction
Please use this identifier to cite or link to this item:
http://hdl.handle.net/1860/1642
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| Title: | Multimodal oscillations in systems with strong contraction |
| Authors: | Medvedev, Georgi
Yoo, Yun |
| Issue Date: | 15-Jan-2007 |
| Publisher: | Elsevier Science B.V. |
| Citation: | Physica D: Nonlinear Phenomena, 228(2): pp. 87-106. Retrieved June 21, 2007 from http://www.math.drexel.edu/~medvedev/papers/. |
| Abstract: | One- and two-parameter families of flows in IR3 near an Andronov-Hopf bifurcation (AHB)
are investigated in this work. We identify conditions on the global vector field, which yield a
rich family of multimodal orbits passing close to a weakly unstable saddle-focus and perform
a detailed asymptotic analysis of the trajectories in the vicinity of the saddle-focus. Our analysis
covers both cases of sub- and supercritical AHB. For the supercritical case, we find that
the periodic orbits born from the AHB are bimodal when viewed in the frame of coordinates
generated by the linearization about the bifurcating equilibrium. If the AHB is subcritical, it
is accompanied by the appearance of multimodal orbits, which consist of long series of nearly
harmonic oscillations separated by large amplitude spikes. We analyze the dependence of the
interspike intervals (which can be extremely long) on the control parameters. In particular,
we show that the interspike intervals grow logarithmically as the boundary between regions of
sub- and supercritical AHB is approached in the parameter space. We also identify a window
of complex and possibly chaotic oscillations near the boundary between the regions of suband
supercritical AHB and explain the mechanism generating these oscillations. This work is
motivated by the numerical results for a finite-dimensional approximation of a free boundary
problem modeling solid fuel combustion. |
| URI: | http://dx.doi.org/10.1016/j.physd.2007.02.011
http://hdl.handle.net/1860/1642 |
| Appears in Collections: | Faculty Research and Publications (Mathematics)
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