Characterization of the attractor governing the neon bulb<i>RC</i>relaxation oscillator

Petrani, M. L.; Karakotsou, Ch.; Kyprianidis, I. Μ.; Anagnostopoulos, A. N.

doi:10.1103/physreve.49.5863

Cited by 6 publications

(1 citation statement)

References 18 publications

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“…For purposes of mathematical analysis, we approximate the I V characteristic of the neon bulb as being a piece-wise linear function V = g(I ) (Petrani et al 1994) as depicted in Fig. 3.…”

Section: The Neon Bulb Modelmentioning

confidence: 99%

Unfolding an electronic integrate-and-fire circuit

Carrillo

Hoppensteadt

2009

Biol Cybern

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Many physical and biological phenomena involve accumulation and discharge processes that can occur on significantly different time scales. Models of these processes have contributed to understand excitability self-sustained oscillations and synchronization in arrays of oscillators. Integrate-and-fire (I+F) models are popular minimal fill-and-flush mathematical models. They are used in neuroscience to study spiking and phase locking in single neuron membranes, large scale neural networks, and in a variety of applications in physics and electrical engineering. We show here how the classical first-order I+F model fits into the theory of nonlinear oscillators of van der Pol type by demonstrating that a particular second-order oscillator having small parameters converges in a singular perturbation limit to the I+F model. In this sense, our study provides a novel unfolding of such models and it identifies a constructible electronic circuit that is closely related to I+F.

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“…For purposes of mathematical analysis, we approximate the I V characteristic of the neon bulb as being a piece-wise linear function V = g(I ) (Petrani et al 1994) as depicted in Fig. 3.…”

Section: The Neon Bulb Modelmentioning

confidence: 99%