Volume: 15, Issue: 5(2005)
pp. 1579-1587 DOI: 10.1142/S0218127405012867
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| Title: |
FOURTH-ORDER NEARLY-SYMMETRIC CNNS EXHIBITING COMPLEX DYNAMICS |
| Author(s): |
M. DI MARCO
Dipartimento di Ingegneria dell'Informazione, Università di Siena, v. Roma 56 – 53100 Siena, ItalyM. FORTI
Dipartimento di Ingegneria dell'Informazione, Università di Siena, v. Roma 56 – 53100 Siena, ItalyM. GRAZZINI
Dipartimento di Ingegneria dell'Informazione, Università di Siena, v. Roma 56 – 53100 Siena, ItalyL. PANCIONI
Dipartimento di Ingegneria dell'Informazione, Università di Siena, v. Roma 56 – 53100 Siena, Italy
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| History: |
Received April 16, 2004
Revised June 10, 2004
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| Abstract: |
In this paper, the possible presence of complex dynamics in nearly-symmetric standard Cellular Neural Networks (CNNs), is investigated. A one-parameter family of fourth-order CNNs is presented, which exhibits a cascade of period-doubling bifurcations leading to the birth of a complex attractor, close to some nominal symmetric CNN. Different from previous work on this topic, the bifurcations and complex dynamics are obtained for small relative errors with respect to the nominal interconnections. The fourth-order CNNs have negative (inhibitory) interconnections between distinct neurons, and are designed by a variant of a technique proposed by Smale to embed a given dynamical system within a competitive dynamical system of larger order. |
| Keywords: |
Cellular Neural Networks; bifurcations; complex dynamics; competitive systems
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