The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective

Şaylı, Mustafa; Skeldon, Anne C.; Thul, Rüdiger; Nicks, Rachel; Coombes, Stephen

doi:10.1016/j.physd.2022.133595

Cited by 7 publications

(1 citation statement)

References 48 publications

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“…Examples in biology include the analysis of one particular type of cardiac arrhythmia, atrioventricular conduction block [8][9][10], investigations of biological mechanisms for sleep-wake regulation [11][12][13][14], the study rhythmic activity of neurons [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

On Forced Oscillations in a Relay System with Hysteresis

Zhusubaliyev,

Sopuev,

Bushuev

2024

ARC

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This paper discusses the phenomenon associated with the forced synchronization (“entrainment of a self-sustained oscillator by an external force”) in a relay system with hysteresis, which manifests itself in the occurrence of periodic motions close to the rhythmic activity of neurons, when packets of fast oscillations are interspersed with intervals of the slow dynamics. To study this phenomenon, we introduce a circle mapping, which, depending on the parameters, can be a circle diffeomorphism or discontinuous map (“gap map”). In both cases, this mapping demonstrates the so-called period-adding bifurcation structure. It is demonstrated that packets number of fast oscillations in the period of periodic motion is determined by the rotation number, and the length of the intervals between the packets may be found of the boundaries of the absorbing interval. The change in the number of pulses in the packet occurs through the border-collision bifurcation.

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