Estimating the locking range of analog dividers through a phase-domain macromodel

Maffezzoni, P.; D'Amore, D.; Daneshgar, Saeid; Kennedy, Michael Peter

doi:10.1109/iscas.2010.5537391

Cited by 4 publications

(1 citation statement)

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“…In fact, respiration and heartbeat in human beings is typically entrained at a 1:4 ratio [70], and evidence exists that human sleep latency is entrained by the lunar cycle [71,72], which is a 1:28 ratio. Other investigations have focused on engineering subharmonic locking in electronic circuits [73,74], antenna systems [75], and voice coil audio systems [76,77].…”

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confidence: 99%

Optimal Subharmonic Entrainment

Zlotnik,

2014

Preprint

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For many natural and engineered systems, a central function or design goal is the synchronization of one or more rhythmic or oscillating processes to an external forcing signal, which may be periodic on a different time-scale from the actuated process. Such subharmonic synchrony, which is dynamically established when N control cycles occur for every M cycles of a forced oscillator, is referred to as N :M entrainment. In many applications, entrainment must be established in an optimal manner, for example by minimizing control energy or the transient time to phase locking. We present a theory for deriving inputs that establish subharmonic N :M entrainment of general nonlinear oscillators, or of collections of rhythmic dynamical units, while optimizing such objectives. Ordinary differential equation models of oscillating systems are reduced to phase variable representations, each of which consists of a natural frequency and phase response curve. Formal averaging and the calculus of variations are then applied to such reduced models in order to derive optimal subharmonic entrainment waveforms. The optimal entrainment of a canonical model for a spiking neuron is used to illustrate this approach, which is readily extended to arbitrary oscillating systems.

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