×

Bifurcation and chaos in noninteger order cellular neural networks. (English) Zbl 0936.92006

Summary: A new class of cellular neural networks (CNNs) is introduced. The peculiarity of the new CNN model consists in replacing the traditional first order cell with a noninteger order one. The introduction of fractional order cells, with a suitable choice of the coupling parameters, leads to the onset of chaos in a two-cell system of a total order of less than three. A theoretical approach, based on the interaction between equilibrium points and limit cycles, is used to discover chaotic motions in fractional CNNs.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
37N25 Dynamical systems in biology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Arena P., IEICE Trans. Fundamentals E79-A (10) pp 1647– (1996)
[2] DOI: 10.1109/9.159595 · Zbl 0825.58027
[3] DOI: 10.1109/31.7600 · Zbl 0663.94022
[4] DOI: 10.1109/31.7601
[5] DOI: 10.1049/ip-d.1991.0042 · Zbl 0754.93024
[6] DOI: 10.1109/81.404062
[7] DOI: 10.1109/PROC.1982.12282
[8] DOI: 10.1103/PhysRevLett.55.529
[9] Oustaloup A., Proc. 3rd European Control Conf. (Rome, Italy) pp 1423– (1995)
[10] DOI: 10.1109/31.81867
[11] DOI: 10.1109/81.222797 · Zbl 0782.92003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.