Synchronization phenomena of two chaotically emitting semiconductor lasers subject to delayed optical feedback are investigated. The lasers are unidirectionally coupled via their optical fields. Our experimental and numerical studies demonstrate that the relative optical feedback phase is of decisive importance: a characteristic synchronization scenario evolves under variation of the relative o...

We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and exampl...

A linear homogeneous scalar diierential{diierence equation with harmonic time dependence is investigated. The associated eigenvalue problem is solved in terms of a continued fraction expansion for the characteristic equation. The dependence of the largest eigenvalue on the system parameters, being relevant for stability of periodic states in delay systems, is discussed in detail. The competitio...

We calculate the Lyapunov exponents in a classical molecular dynamics framework. Yukawa and Slater-Kirkwood forces are considered in order to give an equation of state that resembles the nuclear and the atomic He equation of state, respectively, near the critical point for liquid-gas phase transition. The largest Lyapunov exponents l are always positive and can be very well fitted near the “cri...

Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. As a system parameter changes, chaotic saddles can evolve via an infinite number of homoclinic or heteroclinic tangencies of their stable and unstable manifolds. Based on previous numerical evidence and a rigorous analysis of a class of representative models, we show that dynamical invariants suc...

This work addresses the signal propagation and the fractional-order dynamics during, the evolution of a genetic algorithm (GA), for generating a robot manipulator trajectory. The GA objective is to minimize the trajectory space/time ripple without exceeding the torque requirements. In order to investigate the phenomena involved in the GA population evolution, the mutation is exposed to excitati...

We investigate the physical modifications caused by a linear filter in a chaotic trajectory. We show that while the filter strongly modifies the topological characteristics of the chaotic signal, it might not alter its information content. We propose a chaos-based communication system that takes advantage of this fundamental characteristic of the dynamics. We devise procedures both to recover a...

Using the tools of Differential Geometry, we define a new fast chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e., quickly) than the usual tools, like Lyapunov Characteristic Numbers (LCN’s) or Poincaré Surface of Section. Moreover, at variance with other fast indicators proposed in the Literature, it gives informations about the asymptotic b...

We explain how centrosymmetry, together with a dominant doublet of energy eigenstates in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalization of the chaos-assisted tunnelling mechanism, we formulate a random matrix t...

Since the late 1950’s it has been recognised that the systems used internally within supply chains can lead to oscillations in demand and inventory as orders pass through the system. The uncertainty generated can result in late deliveries, order cancellations and an increased reliance on inventory to buffer these effects. Despite the best efforts of organisations to stabilise the dynamics gener...