Neurons typically show two distinct dynamical regimes: Resting state, corresponding to a stable fixpoint, are often observed for low average input. Higher input commonly result in tonic spiking, which corresponds to a stable limit cycle . Some neurons , however, show an additional intermediate, bistable regime, with coexistence of resting-state fixpoint and limit-cycle spiking . In this article, a bistable neuron with spike onset at a saddle-homoclinic orbit bifurcation is investigated. In the bistable region , noise can switch between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor. This has consequences for spike-time coding as it effectively increases the output entropy of neuronal ensembles. Here, the spiking statistics is derived for homoclinic conductance-based neuron models. Switching between rest and spiking is mainly determined along the downstroke of the action potential , a dynamical feature lacking in common neuron modelswith reset dynamics. Nonetheless similar derivations can be applied to quadratic integrate-and-fire models. The derived interspike interval distribution is shown to be unimodal, which warrants the future use of meanfield approaches to networks of bistable neurons .
Neuronal voltage dynamics of regularly firing neurons typically has one stable attractor: either a fixed point (like in the subthreshold regime) or a limit cycle that defines the tonic firing of action potentials (in the suprathreshold regime). In two of the three spike onset bifurcation sequences that are known to give rise to all-or-none type action potentials , however, the resting-state fixpoint and limit cycle spiking can coexist in an intermediate regime, resulting in bistable dynamics. Here , noise can induce switches between the attractors, i.e., between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor. Qualitative features of the resulting spike statistics depend on the spike onset bifurcations. This study focuses on the creation of the spiking limit cycle via the saddle-homoclinic orbit (HOM) bifurcation and derives interspike interval (ISI) densities for a conductance-based neuron model in the bistable regime. The ISI densities of bistable homoclinic neurons are found to be unimodal yet distinct from the inverse Gaussian distribution associated with the saddle-node-on-invariant-cycle (SNIC) bifurcation. It is demonstrated that for the HOM bifurcation the transition between rest and spiking is mainly determined along the downstroke of the action potential -- a dynamical feature that is not captured by the commonly used reset neuron models. The deduced spike statistics can help to identify HOM dynamics in experimental data .
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Neurons typically show two distinct dynamical regimes: Resting state, corresponding to a stable fixpoint, are often observed for low average input. Higher input commonly result in tonic spiking, which corresponds to a stable limit cycle . Some neurons
Neuronal voltage dynamics of regularly firing neurons typically has one stable attractor: either a fixed point (like in the subthreshold regime) or a limit cycle that defines the tonic firing of action potentials (in the suprathreshold regime). In two of the three spike onset bifurcation sequences that are known to give rise to all-or-none type action potentials
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show an additional intermediate, bistable regime, with coexistence of
the
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limit-cycle spiking . In this article, a bistable neuron with spike onset at a saddle-homoclinic orbit bifurcation is investigated. In the bistable region
limit cycle spiking can coexist in an intermediate regime, resulting in bistable dynamics. Here
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switch between
induce switches between the attractors, i.e., between
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This has consequences for spike-time coding as it effectively increases the output entropy of neuronal ensembles. Here, the spiking statistics is derived for homoclinic
Qualitative features of the resulting spike statistics depend on the spike onset bifurcations. This study focuses on the creation of the spiking limit cycle via the saddle-homoclinic orbit (HOM) bifurcation and derives interspike interval (ISI) densities for a
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models. Switching
model in the bistable regime. The ISI densities of bistable homoclinic neurons are found to be unimodal yet distinct from the inverse Gaussian distribution associated with the saddle-node-on-invariant-cycle (SNIC) bifurcation. It is demonstrated that for the HOM bifurcation the transition
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,
--
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lacking in common neuron modelswith reset dynamics. Nonetheless similar derivations can be applied to quadratic integrate-and-fire models. The derived interspike interval distribution is shown to be unimodal, which warrants the future use of meanfield approaches to networks of bistable neurons
that is not captured by the commonly used reset neuron models. The deduced spike statistics can help to identify HOM dynamics in experimental data