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.


92B20 Neural networks for/in biological studies, artificial life and related topics
37N25 Dynamical systems in biology
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[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
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