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Complex dynamics in the Oregonator model with linear delayed feedback

Abstract : 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
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Submitted on : Monday, March 30, 2009 - 2:11:47 PM
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Krishnamachari Sriram, Samuel Bernard. Complex dynamics in the Oregonator model with linear delayed feedback. Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2008, 18, pp.023126. ⟨10.1063/1.2937015⟩. ⟨hal-00371750⟩



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