Table of Contents
Journal of Nonlinear Dynamics
Volume 2014 (2014), Article ID 710152, 8 pages
http://dx.doi.org/10.1155/2014/710152
Research Article

Catastrophe and Hysteresis by the Emerging of Soliton-Like Solutions in a Nerve Model

1Faculty of Sciences, Autonomous University of the State of Mexico, 50000 Toluca, Mexico
2Department of Applied Mathematics, Russian State Social University, Moscow 129226, Russia

Received 15 June 2014; Revised 6 September 2014; Accepted 13 September 2014; Published 7 October 2014

Academic Editor: Mitsuhiro Ohta

Copyright © 2014 Fernando Ongay Larios et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The nonlinear problem of traveling nerve pulses showing the unexpected process of hysteresis and catastrophe is studied. The analysis was done for the case of one-dimensional nerve pulse propagation. Of particular interest is the distinctive tendency of the pulse nerve model to conserve its behavior in the absence of the stimulus that generated it. The hysteresis and catastrophe appear in certain parametric region determined by the evolution of bubble and pedestal like solitons. By reformulating the governing equations with a standard boundary conditions method, we derive a system of nonlinear algebraic equations for critical points. Our approach provides opportunities to explore the nonlinear features of wave patterns with hysteresis.