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- W2004041898 abstract "With the help of a parallel computer we perform a systematic computation of Lyapunov exponents for a Duffing oscillator driven externally by a force proportional to cos(t). In contrast to the familiar situation in discrete-time systems where one finds “windows” of regularity embedded in intervals of chaos, we find the continuous-time Duffing oscillator to contain a quite regular epetition of relatively self-similar “islands of chaos” (i.e. regions characterized by positive exponents) embedded in large “seas of regularity” (negative exponents). We also investigate the effect of driving the oscillator with a Jacobian elliptic function cn(t, m). For m = 0 one has cn(t, 0) ≡ cos(t), the usual trigonometric pumping. For m = 1 one has cn(t, 1) ≡ sech(t), a hyperbolic pumping. When 0 < m < 1 the Jacobian function is an intermediary double-periodic function with periodicity depending on m and with Fourier spectrum consisting of a regular train of narrow lines with varying envelope. Using m to tune the drive appropriately one may displace the islands of chaos in parameter space. Thus, Jacobian pumping provides a possible way of “cleaning chaos” in regions of the parameter space for periodically driven systems." @default.
- W2004041898 created "2016-06-24" @default.
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- W2004041898 date "1995-12-01" @default.
- W2004041898 modified "2023-09-26" @default.
- W2004041898 title "Lyapunov exponents for a Duffing oscillator" @default.
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- W2004041898 doi "https://doi.org/10.1016/0167-2789(95)00215-4" @default.
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