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Unpredictability of Iteration Destination in an Integrate-and-Fire Circuit |
| DAI Jun1,2;HU Chin-Kun3;CHU Xiang-Sheng1;HE Da-Ren1,3 |
| 1College of Physics Science and Technology, Yangzhou University of China, Yangzhou 225002
2College of Mathematics and Physics, Jiangsu University of Science and Technology of China, Zhenjiang 212003
3Institute of Physics, Academia Sinica, Taipei 11529 |
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| Cite this article: |
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DAI Jun, HU Chin-Kun, CHU Xiang-Sheng et al 2006 Chin. Phys. Lett. 23 2023-2026 |
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Abstract Based on our previous study that discovered a new mechanism of the riddled-like basin appearance in piecewise continuous and noninvertible links of two conservative mappings, and the mechanism being the mixing of different attraction basins on a fat-fractal set, which was addressed as the forbidden region net [Phys. Rev. E 72 (2005) 025201(R)], we show numerically that the riddled-like attraction basins and the new mechanism appear in an integrate-and-fire circuit that can be described by piecewise continuous and noninvertible links of two dissipative mappings. This leads to the fact that vast increase of the precision of the initial condition results in practically no improvement in predictability of the iteration destination. Predictability is usually characterized by examining how error probability in the prediction, f(ε), scales with the precision ε under the initial condition. Typically, f(ε) ～ εα with 0 ≤ α ≤ 1 being the uncertainty exponent. For riddled-like basins, α should be zero, which is in good agreement with the numerical simulation results.
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| Keywords:
05.45.Ac
05.45.Df
07.50.-e
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Published: 01 August 2006
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| PACS: |
05.45.Ac
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(Low-dimensional chaos)
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05.45.Df
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(Fractals)
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07.50.-e
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(Electrical and electronic instruments and components)
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