Mapped clock oscillators as ring devices and their application to neuronal electrical rhythms.
The mapped clock oscillator (MCO) is a second-order, Winfree-type oscillator generating two instantaneous clock variables (amplitude and phase) that are mapped to an observable output variable (voltage) via a static nonlinearity. Two fundamental classes of ring devices are presented. Their respective dynamics give rise to two oscillator forms--the labile clock and the clock--which can be coupled together in various configurations to create higher-order systems with sufficient complexity to capture the dynamics of neuronal assemblies. To demonstrate the applicability of MCOs in modelling neuronal rhythms, a hippocampal network model of four coupled oscillators was constructed and shown to exhibit rhythmic activity of varying complexity, depending on model parameters. The dynamics of the network were quantified through estimation of the maximum lyapunov exponent and the correlation dimension. Synthesis of complex neuronal rhythms may have therapeutic implications. The modular and efficient design of the MCO should facilitate the process of implementing coupled MCO networks in electronic hardware as potential neural prostheses for treating dynamic diseases such as epilepsy.
Zalay
Osbert C
OC
Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON, M5S 3G9, Canada.
Bardakjian
Berj L
BL
D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D005246:Feedback / Q000502:physiology; D006624:Hippocampus / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D009435:Synaptic Transmission / Q000502:physiology*