Subharmonic stochastic synchronization and resonance in neuronal systems.

We study the response of a model neuron, driven simultaneously by noise and at least two weak periodic signals. We focus on signals with frequencies components kf(0),(k+1)f(0),...(k+n)f(0) with k>1. The neuron's output is a sequence of pulses spaced at random interpulse intervals. We find an optimum input noise intensity for which the output pulses are spaced approximately 1/f(0), i.e., there is a stochastic resonance (SR) at a frequency missing in the input. Even higher noise intensities uncover additional, but weaker, resonances at frequencies present in the input. This is a different form of SR whereby the most robust resonance is the one enhancing a frequency, which is absent in the input, and which is not possible to recover via any linear processing. This can be important in understanding sensory systems including the neuronal mechanism for perception of complex tones.

Nonlinear electronic circuit with neuron like bursting and spiking dynamics.

It is difficult to design electronic nonlinear devices capable of reproducing complex oscillations because of the lack of general constructive rules, and because of stability problems related to the dynamical robustness of the circuits. This is particularly true for current analog electronic circuits that implement mathematical models of bursting and spiking neurons. Here we describe a novel, four-dimensional and dynamically robust nonlinear analog electronic circuit that is intrinsic excitable, and that displays frequency adaptation bursting and spiking oscillations. Despite differences from the classical Hodgkin-Huxley (HH) neuron model, its bifurcation sequences and dynamical properties are preserved, validating the circuit as a neuron model. The circuit's performance is based on a nonlinear interaction of fast-slow circuit blocks that can be clearly dissected, elucidating burst's starting, sustaining and stopping mechanisms, which may also operate in real neurons. Our analog circuit unit is easily linked and may be useful in building networks that perform in real-time.