Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems

We discuss the notion of Liapunov exponent for integrate-and-fire (LF) type dynamical systems. In contrast to smooth flows there is a contribution to the IF Liapunov exponent arising from the discontinuous nature of the firin g mechanism. Introducing the notion of an IF mode-locked state we are able to show that linear stability is consistent with the requirement of a negat ive IF Liapunov exponent, We apply our results to IF systems that may be us ed to study the entrainment of biological oscillators. (C) 1999 Elsevier Sc ience B.V. All rights reserved.