An Analytical Method for Piecewise Linear Systems by Vector Fields.

Lorenz and Rössler Systems with Piecewise-Linear Vector Fields

Dynamical systems of class C [1] are described by the 3-order autonomous differential equation with nonlinearity given as a three-segment piecewise linear (PWL) function. Argument of this function is a linear combination of state variables. These systems form an extensive group of nonlinear systems with PWL vector fields and may produce rich set of chaotic attractors. The paper shows how this g...

Piecewise Constant Controlled Linear Fuzzy Systems

Combinatorial Vector Fields for Piecewise Affine Control Systems

This paper is intended to be a continuation of Habets and van Schuppen [2004] and Habets et al. [2006], which address the control problem for piecewise-affine systems on an arbitrary polytope or a family of these. Our work deals with the underlying combinatorics of the underlying discrete system. Motivated by Forman [1998], on the triangulated state space we define a combinatorial vector field,...

Higher Order Singularities in Piecewise Linear Vector Fields

Piecewise linear interpolation of 2D scattered vector data is a classical, simple and fast scheme to process the discrete information provided by experiments or numerical simulations. Nevertheless, its major drawback is its low order that prevents satisfying approximation of non linear behaviors. For topology-based methods in particular, commonly applied in vector field visualization, it often ...

Morse Decomposition of 3D Piecewise Linear Vector Fields

Morse decomposition has been shown a reliable way to compute and represent vector field topology. Its computation first converts the original vector field into a directed graph representation, so that flow recurrent dynamics (i.e., Morse sets) can be identified as some strongly connected components of the graph. In this paper, we present a framework that enables the user to efficiently compute ...