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´_T) ⊂ D´_T and | DT|> 1 on D´_T, where D´_T is some subset in the domain of T and DT is the Jacobian. It implies that T exhibits area-expanding chaotic attractors