Generation of finite wave trains in excitable media

¹  Department of Medicine (Cardiology), University of California - Los Angeles, CA 90095, USA
²  Department of Physics, University of California - Berkeley, CA 94720, USA
³  Department of Physiological Science, University of California - Los Angeles, CA 90095, USA

Corresponding author: yochelis@technion.ac.il

Received: 2 July 2008
Accepted: 11 August 2008

Abstract

Spatiotemporal control of excitable media is of paramount importance in the development of new applications, ranging from biology to physics. To this end, we identify and describe a qualitative property of excitable media that enables us to generate a sequence of traveling pulses of any desired length, using a one-time initial stimulus. The wave trains are produced by a transient pacemaker generated by a one-time suitably tailored spatially localized finite amplitude stimulus, and belong to a family of fast pulse trains. A second family, of slow pulse trains, is also present. The latter are created through a clumping instability of a traveling wave state (in an excitable regime) and are inaccessible to single localized stimuli of the type we use. The results indicate that the presence of a large multiplicity of stable, accessible, multi-pulse states is a general property of simple models of excitable media.