In principle, the state space of a chaotic attractor can be partially or wholly reconstructed from interspike intervals recorded from experiment. Under certain conditions, the quality of a partial reconstruction, as measured by the spike train prediction error, can be increased by adding noise to the spike creation process. This phenomenon for chaotic systems is an analogue of stochastic resona...

In principle, the state space of a chaotic attractor can be partially or wholly reconstructed from interspike intervals recorded from experiment. Under certain conditions, the quality of a partial reconstruction, as measured by the spike train prediction error, can be increased by adding noise to the spike creation process. This phenomenon for chaotic systems is an analogue of stochastic resona...

We propose a method that is able to analyze chaotic time series, gained from experimental data. The method allows to identify scalar time-delay systems. If the dynamics of the system under investigation is governed by a scalar time-delay differential equation of the form dy(t) dt = h(y(t), y(t−τ0)), the delay time τ0 and the function h can be recovered. There are no restrictions to the dimensio...

In this paper, a chaotic switched arrival system is considered. Poincaré section and Poincaré mapping are introduced for defining periodic orbits of this hybrid system. We propose a time-delayed impulsive feedback method to detect unstable periodic orbits embedded in the chaotic attractor. The convergence of the proposed algorithm is proved.

This paper reports the finding of a 3-scroll chaotic attractor with only three equilibria obtained via direct modification of Chua’s circuit. In addition, it is shown numerically that the new system can also generate one-scroll and two-scroll chaotic attractors. PACS numbers: 05.45.-a, 05.45.Gg.

A class of RC-OTA hysteretic-chaotic generators has been proposed from the electronics point of view. Hysteresis is captured by an electronic realization. To extend its applicability, hysteretic mathematical modeling is an important issue. Here, a new hysteretic model is proposed. With this model, we realized a well known hysteretic-chaotic attractor using Simnon.

We present a chaotic frequency-modulated microwave source that is governed by a simple, first-order nonlinear delay differential equation. When a sinusoidal nonlinearity is incorporated, the dynamical behaviors range from fixed-point to periodic to chaotic, depending on the feedback strength. When the sinusoidal nonlinearity is replaced by a binary nonlinearity, the system exhibits a complex pe...

Some nonlinear dynamical techniques, including state-space reconstruction and correlation integral, are used to analyze the light curve of 3C 273. The result is compared with a chaotic model. The similarities between them suggest that there is a low-dimensional chaotic attractor in the light curve of 3C 273.

Chaotic attractors contain unstable periodic orbits of any desired period (this is shown in chapter 22 for Axiom A attractors). Furthermore, for an ergodic attractor we know that any trajectory will eventually come arbitrarily close to any of these orbits. This offers the opportunity for controlling chaos: when the chaotic orbit approaches the unstable periodic orbit of interest it can be attra...