The paper considers the full-range (FR) model of cellular neural networks (CNNs) with ideal hard-limiter non-linearities that limit the allowable range of the neuron state variables. It is also supposed that there is a concentrated delay (D) in the neuron interconnections. Due to the presence of multivalued nonlinearities the D-FRCNN model is mathematically described by a retarded differential inclusion. The main result is a rigorous proof that, in the case of nonsymmetric cooperative (nonnegative) interconnections, and delayed interconnections, the semiflow generated by D-FRCNNs is monotone, and that monotonicity implies some basic restrictions on the long-term behavior of the solutions. The result is compared with recent results in the literature on semiflows generated by cooperative standard CNNs, with and without delays.
DI MARCO, M., Forti, M., Grazzini, M., Pancioni, L. (2012). Monotonicity of semiflows generated by cooperative delayed full-range CNNs. In 13th International Workshop on Cellular Nanoscale Networks and their Applications, CNNA 2012 (pp.1-6). New York : IEEE / Institute of Electrical and Electronics Engineers Incorporated:445 Hoes Lane:Piscataway, NJ 08854:(800)701-4333, (732)981-0060, EMAIL: subscription-service@ieee.org, INTERNET: http://www.ieee.org, Fax: (732)981-9667 [10.1109/CNNA.2012.6331406].
Monotonicity of semiflows generated by cooperative delayed full-range CNNs
DI MARCO, MAURO;FORTI, MAURO;GRAZZINI, MASSIMO;PANCIONI, LUCA
2012-01-01
Abstract
The paper considers the full-range (FR) model of cellular neural networks (CNNs) with ideal hard-limiter non-linearities that limit the allowable range of the neuron state variables. It is also supposed that there is a concentrated delay (D) in the neuron interconnections. Due to the presence of multivalued nonlinearities the D-FRCNN model is mathematically described by a retarded differential inclusion. The main result is a rigorous proof that, in the case of nonsymmetric cooperative (nonnegative) interconnections, and delayed interconnections, the semiflow generated by D-FRCNNs is monotone, and that monotonicity implies some basic restrictions on the long-term behavior of the solutions. The result is compared with recent results in the literature on semiflows generated by cooperative standard CNNs, with and without delays.
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https://hdl.handle.net/11365/48973
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