Homoclinic chaos is characterized by regular geometric orbits occurring at erratic times. Phase synchronization at the average repetition frequency is achieved by a tiny periodic modulation of a control parameter. An experiment has been carried on a CO(2) laser with feedback, set in a parameter range where homoclinic chaos occurs. Any offset of the modulation frequency from the average induces ...

We carry out a systematic study of a different type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one-dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter epsilon...

In billiard systems with a ux line semiclassical approximations for the density of states contain contributions from periodic orbits as well as from diiractive orbits that are scattered on the ux line. We derive a semiclassical approximation for diiractive orbits that are scattered once on a ux line. This approximation is uniformly valid for all scattering angles. The diiractive contributions a...

The paper presents a chaos-based True Random Number Generator (TRNG) implemented in commercially available mixed-signal PSoC reconfigurable devices without any external components. Contrary to the traditionally used sources of randomness (eg various ”well-behaved” analog noise sources) it uses well-defined deterministic analog circuit that exhibits chaos. A new simple method of mapping the dete...

We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Pe clet numbers of...

From an empirical point of view, it is difficult to distinguish between fluctuations provoked by random shocks and endogenous fluctuations determined by the nonlinear nature of the relation between economic aggregates. For this purpose, chaos tests are developed to investigate the chaotic phenomena of basic features: nonlinearity, fractal attractor, and sensitivity to initial conditions. The ap...

The implications of approximate dynamical constants of motion for statistical analysis of highly excited vibrational spectra are investigated. The existence of approximate dynamical constants is related to localized chaos and partial assignability of a "chaotic spectrum." Approximate dynamical constants are discussed in a dynamical symmetry breaking formulation of the transition from periodic t...

[1] The Martian outflow channels were carved by the eruption of catastrophic floods from groundwater aquifers. This study models the time evolution of a typical outflow channel flood originating within a chaos region. The flood initiates when superlithostatic pore pressures within a confined aquifer lead to the propagation of hydrofractures through the confining cryosphere to the surface. The p...