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 diff...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） - ε^α with 0 ≤ α ≤ 1 being the uncertainty exponent. For riddled-like basins, a should be zero, which is in good agreement with the numerical simulation results.展开更多
We investigate a system described by a conservative and a dissipative map concatenation. A fat fractal forbidden net, induced by interaction between discontinuous and noninvertible properties, introduces rippled-like ...We investigate a system described by a conservative and a dissipative map concatenation. A fat fractal forbidden net, induced by interaction between discontinuous and noninvertible properties, introduces rippled-like attraction basins of two periodic attractors. Small areas, which serve as escaping holes of a new type of crisis, are dominated by conventional strong dissipation and are bounded by the forbidden region, but only in the vicinity of each periodic point. Based on this understanding, the scaling behaviour of the averaged lifetime of the crisis is analytically and numerically determined to be （τ） ∝ （b-b0）^γ, where b denotes the control parameter, bo denotes its critical threshold, and γ≌-1.5.展开更多
A new kind of crisis was observed in a system where a transition from conservative to quasi-dissipative can be observed. The crisis signifies a sudden and intrinsic change of a stochastic web, which is formed by the e...A new kind of crisis was observed in a system where a transition from conservative to quasi-dissipative can be observed. The crisis signifies a sudden and intrinsic change of a stochastic web, which is formed by the end-results of the images of the discontinuous borderlines of the system function. In the crisis, a strange quasi-repeller can be defined. When changing the controlling parameter, the variation of the fractile dimension of the quasi-repeller obeys a logarithmic rule.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 10275053. C.-K. Hu and D.-R. He are also supported by the National Science Council in Taiwan under Grant No NSC 93-2112-M 001-027 and the National Center for Theoretical Sciences at Taipei： Physics Division.
文摘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） - ε^α with 0 ≤ α ≤ 1 being the uncertainty exponent. For riddled-like basins, a should be zero, which is in good agreement with the numerical simulation results.
基金Supported by the National Natural Science Foundation of China under Grant No 10275053.
文摘We investigate a system described by a conservative and a dissipative map concatenation. A fat fractal forbidden net, induced by interaction between discontinuous and noninvertible properties, introduces rippled-like attraction basins of two periodic attractors. Small areas, which serve as escaping holes of a new type of crisis, are dominated by conventional strong dissipation and are bounded by the forbidden region, but only in the vicinity of each periodic point. Based on this understanding, the scaling behaviour of the averaged lifetime of the crisis is analytically and numerically determined to be （τ） ∝ （b-b0）^γ, where b denotes the control parameter, bo denotes its critical threshold, and γ≌-1.5.
基金The project supported by the National Natural Science Foundation of China (No.10275053)
文摘A new kind of crisis was observed in a system where a transition from conservative to quasi-dissipative can be observed. The crisis signifies a sudden and intrinsic change of a stochastic web, which is formed by the end-results of the images of the discontinuous borderlines of the system function. In the crisis, a strange quasi-repeller can be defined. When changing the controlling parameter, the variation of the fractile dimension of the quasi-repeller obeys a logarithmic rule.
