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In this paper, we study the dynamical properties of these averaged equations when the homeostatic time scale is close to the synaptic modification time scale.
There are, thus, two essential time scales in the BCM rule: a homeostatic time scale, and a synaptic modification time scale.
Indeed, there is no biological reason why the homeostatic time scale should be dramatically shorter than the synaptic modification time scale [21], so in this paper, we relax those restrictions.
We studied the dynamics and bifurcation structures of these averaged equations when the homeostatic time scale is close to the synaptic modification time scale, and found that instabilities arise, leading to oscillations and in some cases chaos and other complex dynamics.
Although the literature does not suggest a homeostatic time-scale range that ensures stability of a biological system, we have shown that the selective fixed points of the BCM rule are generally stable when the homeostatic time scale is faster than synaptic modification time scale, and that some complex dynamics emerges as the homeostatic time scale varies.
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In many biological processes, the transcription factor transit from inactive to active state quickly as a consequence of fast post-translational modifications, (the time scale is micro second), so it is reasonable that we model the TF activity as a binary variable r(t) ∈{0,1}[ 24, 32].
Scale-up is traduced in practice by an increase of the dimensions of the bioreactors, leading to a modification of the time scale and thus of the process dynamics.
Time-scale modification (TSM): time-scale modification between +5% and of the total audio excerpt length is performed.
Also, the algorithm was not as robust against time scale modification (TSM) and speed change [8].
TSMZ2, TSMF2, TSMZ3, and TSMF3 mean time scale modification under +2%, −2%, +3%, and −3%, respectively.
In this article, the synchronization code is introduced to resist the time scale modification caused by the DA/AD conversions.
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