title: Robust design of polyrhythmic neural circuits.
abstract: Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and other Hodgkin-Huxley-type networks.
authors.affiliation: Neuroscience Institute, Georgia State University, Atlanta, Georgia 30303, USA.
authors.forename: Justus T C
authors.initials: JT
authors.lastname: Schwabedal
authors.affiliation: Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA.
authors.forename: Alexander B
authors.initials: AB
authors.lastname: Neiman
authors.affiliation: Neuroscience Institute, Georgia State University, Atlanta, Georgia 30303, USA and Department of Computational Mathematics and Cybernetics, Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod 603950, Russia.
authors.forename: Andrey L
authors.initials: AL
authors.lastname: Shilnikov
mesh_terms: D000200:Action Potentials / Q000502:physiology; D009010:Monte Carlo Method; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology; D010507:Periodicity; D013269:Stochastic Processes; D013569:Synapses / Q000502:physiology