Through quasiperiodic forcing, an excitable system can be driven into a regime of spiking behavior that is both aperiodic and stable. This is a consequence of strange nonchaotic dynamics: the motion of the system is on a fractal attractor and the largest Lyapunov exponent is negative.

We introduce a stochastic business cycle model and study the underlying stochastic Hopf bifurcations with respect to probability densities at different parameter values. Our analysis is based on the calculate of the largest Lyapunov exponent via multiplicative ergodic theorem and the theory of boundary analysis for quasi-non-integrable Hamiltonian systems. Some numerical simulations of the mode...

In this work we discuss the most recent results concerning the Vlasov dynamics inside the spinodal region. The chaotic behaviour which follows an initial regular evolution is characterized through the calculation of the fractal dimension of the distribution of the final modes excited. The ambiguous role of the largest Lyapunov exponent for unstable systems is also critically

Strange nonchaotic attractors (SNAs) are observed in quasiperiodically driven time–delay systems. Since the largest Lyapunov exponent is nonpositive, trajectories in two such identical but distinct systems show the property of phase–synchronization. Our results are illustrated in the model SQUID and Rössler oscillator systems.

The paper presents the method of predicting the epileptic seizure on the basis of EEG waveform analysis. The Support Vector Machine and the largest Lyapunov exponent characterization of EEG segments are employed to predict the incoming seizure. The results of numerical experiments will be presented and discussed.

This paper, derives sufficient conditions for the existence of chaotic attractors in a general n-D piecewise linear discrete map, along the exact determination of its dynamics using the standard definition of the largest Lyapunov exponent. c © Electronic Journal of Theoretical Physics. All rights reserved.

We derive an upper bound for the largest Lyapunov exponent of a Markovian product of nonnegative matrices using Markovian type counting arguments. The bound is expressed as the maximum of a nonlinear concave function over a finite-dimensional convex polytope of probability distributions. ∗Research supported by ONR MURI N00014-1-0637, DARPA grant No. N66001-00-C8062, and by NSF contract ECS 0123...

We analyse the computability and the complexity of various definitions of spectral radii for sets of matrices. We show that the joint and generalized spectral radii of two integer matrices are not approximable in polynomial time, and that two related quantities – the lower spectral radius and the largest Lyapunov exponent – are not algorithmically approximable.

Sinusoidally driven oscillator equations with a power-law nonlinearity are investigated computationally to determine the driving frequency which produces the “most chaos”, i.e., the maximized largest Lyapunov exponent. It is argued that the “simplest” such driven chaotic oscillator has a cubic nonlinearity x3.  2001 Elsevier Science B.V. All rights reserved. PACS: 05.45.-a; 02.30.Hq

We show that it is possible to devise a large class of skew–product dynamical systems which have strange nonchaotic attractors (SNAs): the dynamics is asymptotically on fractal attractors and the largest Lyapunov exponent is nonpositive. Furthermore, we show that quasiperiodic forcing, which has been a hallmark of essentially all hitherto known examples of such dynamics is not necessary for the...