Eur. Phys. J. B (2014) 87: 108
https://doi.org/10.1140/epjb/e2014-40999-1

Regular Article

Propagating wave segment under global feedback

Department of Complex and Intelligent Systems, School of Systems Information Science, Future University Hakodate, 041-8655 Hakodate, Japan

^a e-mail: satoshi@fun.ac.jp

Received: 12 November 2013
Received in final form: 26 March 2014
Published online: 8 May 2014

Abstract

In this study, we consider a propagating wave segment in two dimensions. A reaction diffusion system with global feedback is proposed, and spiral waves and propagating wave segments are shown. Propagating wave segments with large arc lengths can exist due to the absence of strong lateral inhibition. In order to study the properties of propagating wave segments, we propose a kinematic model with global feedback. When the elongating and shortening effects on the curve are balanced, stable propagating wave segments exist. For other cases, the initial wave segment evolves into a spiral wave or expanding wave or shrinking wave. The conditions for the propagating wave segment and the dependences of the solutions on the various relevant parameters are discussed.