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• W2051210588 startingPage "023126" @default.
• W2051210588 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." @default.
• W2051210588 created "2016-06-24" @default.
• W2051210588 creator A5019492193 @default.
• W2051210588 creator A5038380837 @default.
• W2051210588 date "2008-06-01" @default.
• W2051210588 modified "2023-10-18" @default.
• W2051210588 title "Complex dynamics in the Oregonator model with linear delayed feedback" @default.
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• W2051210588 doi "https://doi.org/10.1063/1.2937015" @default.
• W2051210588 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/18601493" @default.
• W2051210588 hasPublicationYear "2008" @default.
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