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Boolean difference equations. I - Formulation and dynamic behaviorIn many biological and physical systems, feedback mechanisms depend on a set of thresholds associated with the state variables. Each feedback has a characteristic time scale. It is suggested that delay-difference equations for Boolean-valued variables are an appropriate mathematical framework for such situations: the feedback thresholds result in the discrete, on-off character of the variables, and the interaction time scales of the feedbacks are expressed as delays. The initial-value problem for Boolean delay equations (B-Delta-Es) is formulated, and shown to have unique solutions for all times. Examples of periodic and aperiodic solutions are given. Aperiodic solutions have increasing complexity which depends on time t roughly as t to the l-1 power, l being the number of delays. Stability of solutions is defined, and some examples of stability analysis are given; additional stability questions are raised. The present formulation of (B-Delta-Es) is compared with related work and generalizations are suggested.
Document ID
19840042182
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Dee, D.
(New York Univ. New York, NY, United States)
Ghil, M.
(New York University New York, NY, United States)
Date Acquired
August 12, 2013
Publication Date
February 1, 1984
Publication Information
Publication: SIAM Journal on Applied Mathematics
Volume: 44
ISSN: 0036-1399
Subject Category
Cybernetics
Accession Number
84A24969
Funding Number(s)
CONTRACT_GRANT: NSG-5034
CONTRACT_GRANT: NSF ATM-80-18671
CONTRACT_GRANT: NSG-5130
CONTRACT_GRANT: NSF ATM-82-14754
Distribution Limits
Public
Copyright
Other

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