Coexistence of Bursting Regimes
Coexisting bursting solutions are exhibited in some models of bursting (link) neurons. Such solution regimes manifest themselves as a large number (typically three or more) coexisting stable periodic solutions. These solutions coexist at a given fixed parameter set, persist indefinitely, and can be switched by between external perturbations.
Many biological dynamical systems exhibit multistability. Such systems have two or more stable attractors for a fixed set of parameters. Multistable periodic systems exhibit two or more oscillatory attractors for a fixed set of parameters. Examples of multistability can be found in vertebrate motoneurons (e.g., Hounsgaard and Kiehn 1989, where two distinct spike firing rates of action potentials coexist), invertebrate neurons (e.g., Lechner et al. 1996, coexisting bursting and spiking oscillations), and small networks of coupled neurons (e.g., Kleinfeld et al. 1990). Outside of neuroscience, such...
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