A piecewise-linear nerve conduction equation is investigated further. The theory of Poincare halfmaps induced by the flow of a three-dimensional linear saddle-focus is developed. Using a description of the dynamical system in diagonalized coordinates, a canonical formulation of two-dimensional halfmaps is found. This leads for each halfmap to an implicit scalar equation plus a side condition. The effect of the halfmaps on different types of invariant curves occurring is investigated. Thereby the capacity of the halfmaps to separate adjacent points (such that the images acquire a finite distance) is shown. Two of three possible mechanisms for separating points are investigated in detail. The regions in the canonical parameter space where the different separating mechanisms appear are indicated analytically. The possible appearance of chaotic solutions, at least in the neighborhood of homoclinic trajectories in state space, is demonstrated. The underlying separation mechanism is present also in regions of state space far from a homoclinic orbit.
© 1946 – 2014: Verlag der Zeitschrift für Naturforschung
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
