A singular bifurcation into instant chaos in a piecewise-linear circuit
A singular bifurcation into instant chaos in a piecewise-linear circuit
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分段线性电路中奇异分岔导致瞬时混沌
DOI：
10.1109/81.295239
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发表时间：
1994
影响因子：
5.1
通讯作者：
N. Inaba
中科院分区：
文献类型：
--
作者：
M. Ohnishi;N. Inaba
从一个简单的电子电路导出的分段线性二阶非自治微分方程，发现了通向混沌的奇异分岔路径。当一个极限环失去稳定性时，吸引子不经历倍周期分岔或不稳定性，直接变为混沌（瞬时混沌）。在分岔点处，吸引子带的宽度是连续的，混沌带随着系统参数的变化而不断变大。我们称这种分叉为瞬时混沌的奇异分叉。本文的目的是说明奇异现象是由系统的分段线性引起的。为了详细分析这一现象，退化的方法。在这种简化的情况下，庞加莱映射被严格地导出为一维映射。通过分析，我们用计算机辅助证明了在分岔点处，李雅普诺夫指数从负到正不连续地跳变。>
Strange bifurcation route to chaos is found in a piecewise-linear second-order nonautonomous differential equation derived from a simple electronic circuit. When a limit cycle loses its stability, the attractor changes directly to chaos (instant chaos) without undergoing a period doubling bifurcation or an intermittency. The width of the attractor's band is continuous at the bifurcation point, and the chaotic band grows larger continuously as the system parameter is varied. We call this bifurcation a singular bifurcation into instant chaos. The purpose of this paper is to show that the singular phenomenon arises from the piecewise-linearity of the system. To analyze this phenomenon in detail, the degenerate approach is applied. In this simplified case, the Poincare map is derived rigorously as a one-dimensional mapping. By analyzing it, we prove with computer assistance that the Liapunov exponent jumps discontinuously from minus to plus at the bifurcation point. >
DOI：
10.1109/tcs.1986.1085869
发表时间：
1986-11-01
期刊：
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS
影响因子：
--
作者：
CHUA, LO;KOMURO, M;MATSUMOTO, T
通讯作者：
MATSUMOTO, T