Experimental evidence of a hard transition to chaos

A generic, sudden transition to chaos has been experimentally verified using electronic circuits. The particular system studied involves the near resonance of two coupled oscillators at 2:1 frequency ratio when the damping of the first oscillator becomes negative. We identified in the experiment all types of orbits described by theory. We also found that a theoretical, ID limit map fits closely a map of the experimental attractor which, however, could be strongly disturbed by noise. In particular, we found noisy periodic orbits, in good agreement with noise theory.

Damping models in the truncated derivative nonlinear Schrödinger equation

Four-dimensional flow in the phase space of three amplitudes of circularly polarized Alfven waves and one relative phase, resulting from a resonant three-wave truncation of the derivative nonlinear Schrödinger equation, has been analyzed; wave 1 is linearly unstable with growth rate , and waves 2 and 3 are stable with damping 2 and 3, respectively. The dependence of gross dynamical features on the damping model as characterized by the relation between damping and wave-vector ratios, 2 /3, k2 /k3, and the polarization of the waves, is discussed; two damping models, Landau k and resistive k2, are studied in depth. Very complex dynamics, such as multiple blue sky catastrophes and chaotic attractors arising from Feigenbaum sequences, and explosive bifurcations involving Intermittency-I chaos, are shown to be associated with the existence and loss of stability of certain fixed point P of the flow. Independently of the damping model, P may only exist as against flow contraction just requiring.In the case of right-hand RH polarization, point P may exist for all models other than Landau damping; for the resistive model, P may exist for RH polarization only if 2+3/2.

Decomposition driven interface evolution for layers of binary mixtures: I. Model dirivation and base states

Algebraic topology (homology) is used to analyze the state of spiral defect chaos in both laboratory experiments and numerical simulations of Rayleigh-Bénard convection. The analysis reveals topological asymmetries that arise when non-Boussinesq effects are present. The asymmetries are found in different flow fields in the simulations and are robust to substantial alterations to flow visualization conditions in the experiment. However, the asymmetries are not observable using conventional statistical measures. These results suggest homology may provide a new and general approach for connecting spatiotemporal observations of chaotic or turbulent patterns to theoretical models.

Effect of a variable delay in delayed dynamical systems

We report numerical evidence of the effects of a periodic modulation in the delay time of a delayed dynamical system. By referring to a Mackey-Glass equation and by adding a modula- tion in the delay time, we describe how the solution of the system passes from being chaotic to shadow periodic states. We analyze this transition for both sinusoidal and sawtooth wave mod- ulations, and we give, in the latter case, the relationship between the period of the shadowed orbit and the amplitude of the modulation. Future goals and open questions are highlighted.

Defect chaos and bursts: Hexagonal rotating convection and the complex Ginzburg-Landau equation

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.

Reentrant hexagons in non-Boussinesq convection.

While non-Boussinesq hexagonal convection patterns are known to be stable close to threshold (i.e. for Rayleigh numbers R ? Rc ), it has often been assumed that they are always unstable to rolls for slightly higher Rayleigh numbers. Using the incompressible Navier?Stokes equations for parameters corresponding to water as the working fluid, we perform full numerical stability analyses of hexagons in the strongly nonlinear regime ( ? (R ? Rc )/Rc = O(1)). We find ?re-entrant? behaviour of the hexagons, i.e. as is increased they can lose and regain stability. This can occur for values of as low as = 0.2. We identify two factors contributing to the re-entrance: (i) far above threshold there exists a hexagon attractor even in Boussinesq convection as has been shown recently and (ii) the non-Boussinesq effects increase with . Using direct simulations for circular containers we show that the re-entrant hexagons can prevail even for sidewall conditions that favour convection in the form of competing stable rolls. For sufficiently strong non-Boussinesq effects hexagons even become stable over the whole -range considered, 0 6 6 1.5.

Chaos synchronization in optically programmable logic cells

A possible approach to the synchronization of chaotic circuits is reported. It is based on an Optically Programmable Logic Cell and the signals are fully digital. A method to study the characteristics of the obtained chaos is reported as well as a new technique to compare the obtained chaos from an emitter and a receiver. This technique allows the synchronization of chaotic signals. The signals received at the receiver, composed by the addition of information and chaotic signals, are compared with the chaos generated there and a pure information signal can be detected. Its application to cryptography in Optical Communications comes directly from these properties. The model here presented is based on a computer simulation.

Sequences of bifurcations and transition to chaos in an optical processing element

Digital chaotic behaviour in an Optical-Processing Element is reported. It is obtained as the result of processing two fixed trains of bits. Period doublings in a Feigenbaum-like scenario have been obtained. A new method to characterize digital chaos is reported

Digital chaos analysis in optical logic structures

Digital chaotic behavior in an optically processing element is analyzed. It was obtained as the result of processing two fixed trains of bits. The process is performed with an optically programmable logic gate. Possible outputs, for some specific conditions of the circuit, are given. Digital chaotic behavior is obtained, by using a feedback configuration. Different ways to analyze a digital chaotic signal are presented.

Coherent excitation of nonlinear oscillators

Coherently driven, dissipative nonlinear oscillators,(driving kept permanently in phase with the oscillators response) are proposed as systems with interesting dynamics. Results for simple, preliminary examples, which do not show chaotic behavior, are briefly discussed.

Optically Induced Reorientation in Nematic Cylindrical Structures

Cyclindrical structures of nematics give rise to several opto-optical effects related to molecular reorientation. One of these effects is the formation of diffraction ring patterns similar to the ones observed in planar cells, but differing in shape. Another effect has been observed, namely a quasi-chaotic motion of rings with a very large angular spread; this motion can be obtained using a cw laser and high power densities. The phenomenon could be attributed to thermal motion, however, there are some features that cannot be explained by a purely thermal effect, e.g., a wavelength dependence of the threshold and the frequencies of the ring motion.

Optical digital chaos cryptography

In this work we present a new way to mask the data in a one-user communication system when direct sequence - code division multiple access (DS-CDMA) techniques are used. The code is generated by a digital chaotic generator, originally proposed by us and previously reported for a chaos cryptographic system. It is demonstrated that if the user's data signal is encoded with a bipolar phase-shift keying (BPSK) technique, usual in DS-CDMA, it can be easily recovered from a time-frequency domain representation. To avoid this situation, a new system is presented in which a previous dispersive stage is applied to the data signal. A time-frequency domain analysis is performed, and the devices required at the transmitter and receiver end, both user-independent, are presented for the optical domain.

Self-beating instabilities in bistable devices

Since the observation of optical bistability by Gibbs et al., optical bistability has been the field where researchers from many fields have found a common place to work. More recently, when Ikeda and co-workers discussed the effect of a delayed feedback on instability of a ring cavity containing a non linear dielectric medium, and pointed out that the transmitted light from the ring cavity can be periodic or chaotic in time under a certain condition, optical bistable devices have shown new possibilities to be applied in many different fields. The novel phenomenon has been predicted to be observed in the hybrid optical device and has been confirmed by Gibbs et al. Moreover, as we have shown, a similar effect can be obtained when liquid crystal cells are employed as non linear element.

Coder/decoder with an optical programmable logic cell

A major research area is the representation of knowledge for a given application in a compact manner such that desired information relating to this knowledge is easily recoverable. A complicated procedure may be required to recover the information from the stored representation and convert it back to usable form. Coder/decoder are the devices dedicated to that task. In this paper the capabilities that an Optical Programmable Logic Cell offers as a basic building block for coding and decoding are analyzed. We have previously published an Optically Programmable Logic Cells (OPLC), for applications as a chaotic generator or as basic element for optical computing. In optical computing previous studies these cells have been analyzed as full-adder units, being this element a basic component for the arithmetic logic structure in computing. Another application of this unit is reported in this paper. Coder and decoder are basic elements in computers, for example, in connections between processors and memory addressing. Moreover, another main application is the generation of signals for machine controlling from a certain instruction. In this paper we describe the way to obtain a coder/decoder with the OPLC and which type of applications may be the best suitable for this type of cell.

Logic cells as basic structures to add/drop WDM information signals

Nowadays, in order to take advantage of fiber optic bandwidth, any optical communications system tends to be WDM. The way to extract a channel, characterized by a wavelength, from the optical fiber is to filter the specific wavelength. This gives the systems a low degree of freedom due to the fact of the static character of most of the employed devices. In this paper we will present a different way to extract channels from an optical fiber with WDM transmission. The employed method is based on an Optically Programmable Logic Cells (OPLC) previously published by us, for other applications as a chaotic generator or as basic element for optical computing. In this paper we will describe the configuration of the OPLC to be employed as a dropping device. It acts as a filter because it will extract the data carried by a concrete wavelength. It does depend, internally, on the wavelength. We will show how the intensity of the signal is able to select the chosen information from the line. It will be also demonstrated that a new idea of redundant information it is the way of selecting the concrete wavelength. As a matter of fact this idea is apparently the only way to use the OPLC as a dropping device. Moreover, based on these concepts, a similar way to route signals to different routes is reported. The basis is the use of photonic switching configurations, namely Batcher or Bayan structures, where the unit switching cells are the above indicated OPLCs.