Three-segment Piecewise-linear Vector Fields with Orthogonal Eigenspaces

In the upcoming article eight new members of the dynamical systems of class C and F are investigated via numerical integration. Although four configurations of the state matrices are familiar with the chaos generation the others are hypothetic and complete the study. The aim of this paper is to discover and describe different canonical representations for a given set of the differential equations, i.e. existing mathematical model. Individual dynamical systems are distinct from the viewpoint of the geometry of the associated vector field. The motivation for discovering the new mathematical models capable to produce a complex dynamics including chaos is both pedagogical and practical. The latter case is obvious since the new system can be easier to be implemented as an electronic circuit or has other advantage like simpler location of strategic orbits.