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On the Conditions for the Passage of a Signal Through a Chain of Asynchronous Threshold Elements

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Abstract

We investigate the signal propagation process in a chain of series-connected asynchronous threshold elements. The asynchronous nature of the elements is manifested in the fact that they can have varying duration of switching from a passive state to an active state and vice versa. The elements are reactive; i.e., they are excited as a result of external influences and become passive when there are no external influences. It is shown that, depending on the element on-off switching transient duration ratio, the duration of the signal passing through the chain can be preserved, increase, or decrease. In the last case, the signal does not pass through a sufficiently long chain. The conditions for the passage of a signal through the chain are stated.

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Notes

  1. Asynchronous threshold elements were first considered in [1, 2]. In [1], they were called neurons and in [2], agents.

  2. The papers [1, 2] deal with multisorted broadcast communications—a signal of a particular sort is perceived by all elements that have inputs sensitive to that sort. In the present paper, all signals are ordinary single-sorted signals, and the connections are local, i.e., connect exactly two elements each.

  3. In Fig. 1, already the output signal \( N_1 \) is short for \( N_2 \).

  4. This equality coincides with (23) up to the change of sign on the left-hand side. The remaining proof of Lemma 4 also reproduces the proof of Lemma 3 up to sign change.

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Funding

This work was financially supported in part by the Russian Foundation for Basic Research, project no. 20-07-00190.

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  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    O. P. Kuznetsov

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  1. O. P. Kuznetsov
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Correspondence to O. P. Kuznetsov.

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Translated by V. Potapchouck

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Kuznetsov, O.P. On the Conditions for the Passage of a Signal Through a Chain of Asynchronous Threshold Elements. Autom Remote Control 83, 919–934 (2022). https://doi.org/10.1134/S0005117922060091

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