An approach toward higher dimensional autonomous chaotic circuits is discussed. Special consideration is given to a particular class of circuits which includes only one nonlinear element, namely, a three-segment piecewise-linear resistor, and one small inductor, L/sub 0/, serially connected with it. A simple four-dimensional example that realizes hyperchaos is given. For the case in which L/sub 0/ is shorted, the circuit equation can be simplified to a constrained system and a two-dimensional Poincare map can be rigorously derived. This mapping and its Lyapunov exponents verify laboratory measurements of hyperchaos and related phenomena. A rigorous approach to the singular perturbation theory of an N-dimensional circuit family that includes the above example is then provided. A canonical equation which describes any circuit in this family is derived. This equation can also be simplified to a constrained system, and an (Nn-2)-dimensional Poincare map can be derived. The main theorem indicates that this mapping explains the observable solutions of the canonical form very well.
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机译:讨论了一种针对高维自治混沌电路的方法。特别考虑到一类特定的电路,该电路仅包括一个非线性元件,即三段分段线性电阻器,和一个与其串联的小电感器L / sub 0 /。给出了一个实现超混沌的简单四维示例。对于L / sub 0 /短路的情况,可以将电路方程式简化为一个受约束的系统,并可以严格导出二维Poincare映射。此映射及其Lyapunov指数验证了超混沌和相关现象的实验室测量结果。然后提供了一个严格的方法来解决包含以上示例的N维电路族的奇异摄动理论。得出描述该系列中任何电路的规范方程。也可以将该方程简化为受约束的系统,并可以导出(Nn-2)维庞加莱图。主定理表明,这种映射很好地解释了规范形式的可观察解。
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