Extracting dynamics from threshold-crossing interspike intervals: Possibilities and limitations

In this paper we estimate dynamical characteristics of chaotic attractors f rom sequences of threshold-crossing interspike intervals, and study how the choice of the threshold level (which sets the equation of a secant plane) influences the results of the numerical computations. Under quite general c onditions we show that the largest Lyapunov exponent can be estimated from a series of return times to the secant plane, even in the case when some of the loops of the phase space trajectory fail to cross this plane.