title: Multistable jittering in oscillators with pulsatile delayed feedback.
abstract: Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in recent years. For such systems, we report a remarkable scenario of destabilization of a periodic regular spiking regime. At the bifurcation point numerous regimes with nonequal interspike intervals emerge. We show that the number of the emerging, so-called "jittering" regimes grows exponentially with the delay value. Although this appears as highly degenerate from a dynamical systems viewpoint, the "multijitter" bifurcation occurs robustly in a large class of systems. We observe it not only in a paradigmatic phase-reduced model, but also in a simulated Hodgkin-Huxley neuron model and in an experiment with an electronic circuit.
authors.affiliation: Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia.|University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950 Nizhny Novgorod, Russia.
authors.forename: Vladimir
authors.initials: V
authors.lastname: Klinshov
authors.affiliation: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.
authors.forename: Leonhard
authors.initials: L
authors.lastname: Lücken
authors.affiliation: Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia.|University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950 Nizhny Novgorod, Russia.
authors.forename: Dmitry
authors.initials: D
authors.lastname: Shchapin
authors.affiliation: Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia.|University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950 Nizhny Novgorod, Russia.
authors.forename: Vladimir
authors.initials: V
authors.lastname: Nekorkin
authors.affiliation: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.
authors.forename: Serhiy
authors.initials: S
authors.lastname: Yanchuk
mesh_terms: D001683:Biological Clocks; D005246:Feedback; D008959:Models, Neurological; D008962:Models, Theoretical; D009474:Neurons / Q000502:physiology