Reality of chaos in four-dimensional hysteretic circuits

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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