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    Title: Bifurcations and chaos in two-cell cellular neural networks with periodic inputs
    Authors: Lin, Song-sun;Lin, Wen-wei;楊定揮;Yang, Ting-hui
    Contributors: 淡江大學數學學系
    Keywords: Cellular neural networks;CNN;chaos;crises;fractal;Lady's shoe;Lyapunov exponent
    Date: 2004-09
    Issue Date: 2010-01-28 07:03:50 (UTC+8)
    Publisher: World Scientific Publishing
    Abstract: 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.
    Relation: International Journal of Bifurcations and Chaos 14(9), pp.3179-3204
    DOI: 10.1142/S021812740401134X
    Appears in Collections:[數學學系暨研究所] 期刊論文

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