This paper gives rigorous evidence for chaos in a certain class of four-dimensional hysteretic circuits. The circuit dynamics are described by two symmetric three-dimensional linear equations which are connected to each other by hysteresis switchings. The author transforms the circuit equation into the Jordan form and derives the two-dimensional return map T. Then the author proves a sufficient condition for T(D'/sub T/) contained in/implied by D'/sub T/ and mod DT mod < 1 on D'/sub T/, where D'/sub T/ is some subset in the domain of T and DT is the Jacobian. It implies that T exhibits area-expanding chaotic attractors.
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机译：本文为一类四维滞回电路中的混沌提供了严格的证据。电路动力学由两个对称的三维线性方程式描述，它们通过磁滞开关相互连接。作者将电路方程式转换为约旦形式，并得出二维返回图T。然后作者证明了D'/ sub T /和mod中包含的T（D'/ sub T /）的充分条件。 D'/ sub T /上的DT mod <1，其中D'/ sub T /是T的某个子集，而DT是雅可比行列式。这意味着T表现出面积扩大的混沌吸引子。
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