Complex dynamics in the Oregonator model with linear delayed feedback
| Autor: | Krishnamachari Sriram, Samuel Bernard |
|---|---|
| Přispěvatelé: | Constraint programming (CONTRAINTES), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institute of Applied and Computational Mathematics (IACM), Foundation of Research and Technology?Hellas |
| Rok vydání: | 2008 |
| Předmět: |
Phase portrait
Applied Mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] General Physics and Astronomy Statistical and Nonlinear Physics 01 natural sciences Nullcline 010305 fluids & plasmas Complex dynamics Classical mechanics Belousov–Zhabotinsky reaction Quasiperiodic function 0103 physical sciences Amplitude death 010306 general physics Mathematical Physics Bifurcation Oregonator Mathematics |
| Zdroj: | Chaos: An Interdisciplinary Journal of Nonlinear Science Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2008, 18, pp.023126. ⟨10.1063/1.2937015⟩ Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008, 18, pp.023126. ⟨10.1063/1.2937015⟩ |
| ISSN: | 1089-7682 1054-1500 |
| DOI: | 10.1063/1.2937015 |
| Popis: | International audience; The Belousov-Zhabotinsky (BZ) reaction can display a rich dynamics when a delayed feedback is applied. We used the Oregonator model of the oscillating BZ reaction to explore the dynamics brought about by a linear delayed feedback. The time-delayed feedback can generate a succession of complex dynamics: period-doubling bifurcation route to chaos; amplitude death; fat, wrinkled, fractal, and broken tori; and mixed-mode oscillations. We observed that this dynamics arises due to a delay-driven transition, or toggling of the system between large and small amplitude oscillations, through a canard bifurcation. We used a combination of numerical bifurcation continuation techniques and other numerical methods to explore the dynamics in the strength of feedback-delay space. We observed that the period-doubling and quasiperiodic route to chaos span a low-dimensional subspace, perhaps due to the trapping of the trajectories in the small amplitude regime near the canard; and the trapped chaotic trajectories get ejected from the small amplitude regime due to a crowding effect to generate chaotic-excitable spikes. We also qualitatively explained the observed dynamics by projecting a three-dimensional phase portrait of the delayed dynamics on the two-dimensional nullclines. This is the first instance in which it is shown that the interaction of delay and canard can bring about complex dynamics. ©2008 American Institute of Physics |
| Databáze: | OpenAIRE |
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