Brownian motion driven by a chaotic sequence of iterates of a map F(y), which may depend on a bifurcation parameter, is discussed: 6(t)= -yv(t)+ f(t), where f(t)= Kyn, ~ for nr < t <~ (n + 1)r (n = 0, 1,2 .... ) and y,,\_~ = F(y,,). The time evolution equation for the distribution function of the ve
Resonance phenomena in a harmonic oscillator driven by the chaotic force
โ Scribed by Toshihiro Shimizu
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 651 KB
- Volume
- 234
- Category
- Article
- ISSN
- 0378-4371
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โฆ Synopsis
The coherent nature of chaos is investigated in a simple harmonic oscillator driven by the chaotic force. The resonance phenomena between a harmonic oscillator and a chaotic oscillator are discussed in two cases: (a) the bifurcation parameter of the chaotic force is modulated by the amplitude of the harmonic oscillator and (b) the eigenfrequency of the harmonic oscillator is also modulated by the chaotic force in addition to (a). As a model of neural network, a system of many Brownian particles interacting via the chaotic force is proposed. The controlling of chaos is also discussed.
๐ SIMILAR VOLUMES
When a simple harmonic oscillator is subjected to a sinusoidally varying external force whose frequency is different from the natural frequency of the oscillator, there is a simple and well-known phase relation between the purely forced response and the forcing function. They will have the same or
A harmonic oscillator with time-dependent force constant when perturbed by a weak static quartic anharmonicity ti4, 1 small, is shown to generate new features in the dynamics. For weak coupling, both time-dependent perturbation theoretical analysis and near-exact numerical calculations predict that