| Bifurcations and chaos in two-cell cellular neural networks with periodic inputs | |
|---|---|
| 學年 | 93 |
| 學期 | 1 |
| 出版（發表）日期 | 2004-09-01 |
| 作品名稱 | Bifurcations and chaos in two-cell cellular neural networks with periodic inputs |
| 作品名稱（其他語言） | |
| 著者 | Lin, Song-sun; Lin, Wen-wei; 楊定揮; Yang, Ting-hui |
| 單位 | 淡江大學數學學系 |
| 出版者 | World Scientific Publishing |
| 著錄名稱、卷期、頁數 | International Journal of Bifurcations and Chaos 14(9), pp.3179-3204 |
| 摘要 | This study investigates bifurcations and chaos in two-cell Cellular Neural Networks (CNN) with periodic inputs. Without the inputs, the time periodic solutions are obtained for template A=[r,p,s] with p>1, r>p-1 and -s>p-1. The number of periodic solutions can be proven to be no more than two in exterior regions. The input is bsin2πt/T with period T>0 and amplitude b>0. The typical trajectories Γ(b,T,A) and their ω-limit set ω(b,T,A) vary with b, T and A are also considered. The asymptotic limit cycles Λ∞(T,A) with period T of Γ(b,T,A) are obtained as b→∞. When (given in (67)), Λ∞ and -Λ∞ can be separated. The onset of chaos can be induced by crises of ω(b,T,A) and -ω(b,T,A) for suitable T and b. The ratio , of largest amplitude a1(b) except for T-mode and amplitude of the T-mode of the Fast Fourier Transform (FFT) of Γ(b,T,A), can be used to compare the strength of sustained periodic cycle Λ0(A) and the inputs. When , Λ0(A) dominates and the attractor ω(b,T,A) is either a quasi-periodic or a periodic. Moreover, the range b of the window of periodic cycles constitutes a devil's staircase. When , finitely many chaotic regions and window regions exist and interweave with each other. In each window, the basic periodic cycle can be identified. A sequence of period-doubling is observed to the left of the basic periodic cycle and a quasi-periodic region is observed to the right of it. For large b, the input dominates, ω(b,T,A) becomes simpler, from quasi-periodic to periodic as b increases. |
| 關鍵字 | Cellular neural networks;CNN;chaos;crises;fractal;Lady's shoe;Lyapunov exponent |
| 語言 | en |
| ISSN | 0218-1274 |
| 期刊性質 | 國外 |
| 收錄於 | |
| 產學合作 | |
| 通訊作者 | |
| 審稿制度 | 否 |
| 國別 | SGP |
| 公開徵稿 | |
| 出版型式 | ,紙本 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41245 ) |
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