Motivated by real-world excitable systems such as neuron models and lasers, we consider a paradigmatic model for excitability with a global bifurcation, namely a saddle-node bifurcation on a limit cycle. We study the effect of a time-delayed feedback force in the form of the difference between a system variable at a certain time and at a delayed time. In the absence of delay the only attractor in the system in the excitability regime, below the global bifurcation, is a stable node. Delay renders the phase space infinite-dimensional and creates multistability of periodic orbits and the fixed point. Homoclinic bifurcations, period-doubling as well as saddle-node bifurcations of limit cycles are found in accordance with Shilnikov’s theorems.
- Design Engineering Division and Computers and Information in Engineering Division
Delay-Induced Multistability in a Generic Model for Excitable Dynamics
Hizanidis, J, Aust, R, & Scho¨ll, E. "Delay-Induced Multistability in a Generic Model for Excitable Dynamics." Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C. Las Vegas, Nevada, USA. September 4–7, 2007. pp. 687-694. ASME. https://doi.org/10.1115/DETC2007-34329
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