Lyapunov exponents of a dynamical system give information about its long-term evolution. Exponents estimation is not an easy task; it is computationally costly and, in presence of chaotic dynamics, it exhibits numerical difficulties. In a previous paper, the authors proposed an algorithm for Lyapunov exponents estimation in piecewise linear systems that strongly reduces the computational time. ...

This paper studies a chaotic spiking oscillator consisting of two capacitors, two voltage-controlled current sources of signum shape and one impulsive switch. The vector field of circuit equation is piecewise constant and embedded return map is piecewise linear. Using the map parameter condition for chaos generation is given. Using a simple test circuit typical phenomena can be confirmed experi...

We show that continuous-time chaos can be defined using linear dynamics and represented by an exact analytic solution. A driven linear differential equation is used to define a low-dimensional chaotic set of continuous-time waveforms. A nonlinear differential equation is derived for which these waveforms are exact analytic solutions. This nonlinear system describes a chaotic semiflow with a ret...

This paper and its companion (Part II) are devoted to the analysis of the application of a chaotic piecewise-linear onedimensional (PL1D) map as random number generator (RNG). Piecewise linearity of the map enables us to mathematically find parameter values for which a generating partition is Markov and the RNG behaves as a Markov information source, and then to mathematically analyze the infor...

This paper presents a spiking neuron circuit with a triangular base signal. The circuit can output rich pulse-trains and the dynamics can be analyzed using a piecewise linear one-dimensional pulse-position map. Applying cross-switching to two neurons we construct a pulse-coupled system whose dynamics can be integrated into a composite map of the pulse position maps of two neurons. The composite...

We study the effect of speedup on the dynamical behavior of a single cyclic bus in a bus system with many bus stops. We present a nonlinear-map model of a cyclic bus to take into account the speedup. When the cyclic bus is delayed, the bus speeds up to retrieve the delay. It is found that the cyclic bus exhibits chaotic motion with increasing speedup. The chaotic motion depends on both speedup ...

In a recent letter [Phys.Rev.Lett. 30, 3269 (1995)], we reported that a macroscopic chaotic determinism emerges in a multistable system: the unidirectional motion of a dissipative particle subject to an apparently symmetric chaotic noise occurs even if the particle is in a spatially symmetric potential. In this paper, we study the global dynamics of a dissipative particle by investigating the b...

a chaotic optimization algorithm (coa) based approach for the robust coordinated design of the upfc power oscillation damping controller and the conventional power system stabilizer has been investigated in this paper. chaotic optimization algorithms, which have the features of easy implementation, short execution time and robust mechanisms of escaping from local optimum, is a promising tool fo...