Algebraic determination of limit cycles in a family of three-dimensional piecewise linear differential systems

We study a one-parameter family of symmetric piecewise linear differential systems in R3 which is relevant in control theory. The family, which has some intersection points with the adimensional family of Chua’s circuits, exhibits more than one attractor even when the two matrices defining its dynamics in each zone are stable, in an apparent contradiction to the three-dimensional Kalman’s conjecture.