title: Extracting dynamics from threshold-crossing interspike intervals: possibilities and limitations.
abstract: In this paper we estimate dynamical characteristics of chaotic attractors from 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 conditions 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.
authors.affiliation: Department of Physics, Saratov State University, Russia.
authors.forename: A N
authors.initials: AN
authors.lastname: Pavlov
authors.forename: O V
authors.initials: OV
authors.lastname: Sosnovtseva
authors.forename: E
authors.initials: E
authors.lastname: Mosekilde
authors.forename: V S
authors.initials: VS
authors.lastname: Anishchenko
mesh_terms: D000465:Algorithms; D008954:Models, Biological; D008962:Models, Theoretical; D017711:Nonlinear Dynamics