Arena P, Fortuna L, Porto D
Dipartimento Elettrico Elettronico e Sistemistico, Universita degli Studi di Catania, viale A. Doria 6, 95125 Catania, Italy.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jan;61(1):776-81. doi: 10.1103/physreve.61.776.
In this paper, a simple system showing chaotic behavior is introduced. It is based on the well-known concept of cellular neural networks (CNNs), which have already given good results in generating complex dynamics. The peculiarity of the CNN model consists in the fact that it replaces the traditional first-order cell with a noninteger-order one. The introduction of the fractional cell, with a suitable choice of the coupling parameters, leads to the onset of chaos in a simple two-cell system. A theoretical approach, based on the harmonic balance theory, has been used to investigate the existence of chaos. A circuit realization of the proposed fractional two-cell chaotic CNN is reported and the corresponding strange attractor is also shown.
本文介绍了一个表现出混沌行为的简单系统。它基于细胞神经网络（CNN）这一著名概念，该概念在生成复杂动力学方面已取得良好成果。CNN模型的独特之处在于它用非整数阶的单元取代了传统的一阶单元。通过适当选择耦合参数引入分数阶单元，会导致一个简单的双单元系统出现混沌。已采用基于谐波平衡理论的理论方法来研究混沌的存在性。报道了所提出的分数阶双单元混沌CNN的电路实现，并展示了相应的奇怪吸引子。
