A hysteresis hyperchaos generator family

This article discusses a four dimensional autonomous circuit family that includes one hysteresis element. We derive theoretical formulae of the two dimensional return map, its Jacobian matrix and its Jacobian and show the following novel results: (1) classification of the phenomena by evaluation of Lyapunov exponents using the formulae; (2) period doubling route to chaos and the transition to hyperchaos via crisis; (3) basic bifurcation of these phenomena; and (4) implementation example and laboratory measurements of some attractors.