In order to explain the occurrence of a minimum in firing rate which occurs for certain mean input levels μ as noise level σ increases (inverse stochastic resonance, ISR) in Hodgkin–Huxley (HH) systems, we analyze the underlying transitions from a stable equilibrium point to limit cycle and...

We consider a classical space-clamped Hodgkin–Huxley (HH) model neuron stimulated by a current which has a mean μ together with additive Gaussian white noise of amplitude σ. A system of 14 deterministic first-order nonlinear differential equations is derived for the first- and second-order...

We consider a general nonlinear diffusion, typified by those deriving from Fitzhugh–Nagumo or Hindmarsh–Rose models of nerve-cell dynamics, perturbed also by 2-parameter white noise. In order to investigate the effects of the nonlinearity, we find for general boundary conditions the mean to...

We consider a new and extended spatial neuron model in which the neuronal electrical depolarization from resting level satisfies a cable partial differential equation. The synaptic input current is also a function of space and time and satisfies a first order linear partial differential equation...

The time to first spike is an experimentally observed quantity in laboratory experiments. In the auditory, somatic and visual sensory modalities, the times of first spikes in the corresponding cortical neurons have been implicated as coding much of the information about stimulus properties. We...