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.

Geometric diagnostics of complex patterns: Spiral defect chaos

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripelike patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh- Bénard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers. In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.

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

Determination of critical slip surfaces using mutative scale chaos optimization

Limit equilibrium is a common method used to analyze the stability of a slope, and minimization of the factor of safety or identification of critical slip surfaces is a classical geotechnical problem in the context of limit equilibrium methods for slope stability analyses. A mutative scale chaos optimization algorithm is employed in this study to locate the noncircular critical slip surface with Spencer’s method being employed to compute the factor of safety. Four examples from the literature—one homogeneous slope and three layered slopes—are employed to identify the efficiency and accuracy of this approach. Results indicate that the algorithm is flexible and that although it does not generally provide the minimum FS, it provides results that are close to the minimum, an improvement over other solutions proposed in the literature and with small relative errors with respect to other minimum factor of safety (FS) values reported in the literature.

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Ecological chaos in the wake of invasion.

Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is generated naturally in the wake of invasive waves of predators. We discuss in detail the mechanism by which the chaos is generated. By considering a mathematical caricature of the predator-prey models, we go on to explain the dynamical origin of the irregular behavior and to justify our assertion that the behavior we present is a genuine example of spatiotemporal chaos.

Bosniacki chaos. Zrodla kryzysu politycznego we wspolczesnej Bosni i Hercegowinie. Prace OSW 31/2009. = Bosnia's chaos. Causes of the political crisis in Bosnia and Herzegovina today. OSW Study 31/2009

A new form of 'transformational crisis' has been observed in Bosnia and Herzegovina since at least 2005. Politicians representing the three major ethno-political communities (Bosnians, Croats and Serbs) have successively been raising disputes and have employed various political tools to preserve the conflicts instead of resolving them. As a result, the central state institutions and organisations have been weakened and attempts to replace them with narrower ethnic structures have been made. This is increasingly paralysing the state, thus impeding its everyday operation and preventing its structures and legislation from being modernised; had this been achieved, it would have resulted in a real acceleration of the process of Bosnia's integration with the EU and NATO. The present crisis is also an effect of the disagreement between the key international players - the European Union, the United States and Russia - over the 'plan for Bosnia' and the role and duties of the Office of the High Representative, who acts on behalf of the international community in the country.

Evolution of life from chaos to Christ; Easter offering, by Conrad Siem.

Mode of access: Internet.

Effect of knee joint angle on motor unit synchronization

Activity of the vasti has been argued to vary through knee range of movement due to changes in passive support of the patellofemoral joint and the relative contribution of these muscles to knee extension. Efficient function of the knee is dependent on optimal control of the patellofemoral joint, largely through coordinated activity of the medial and lateral quadriceps. Motor unit synchronization may provide a mechanism to coordinate the activity of vastus medialis (VMO) and vastus lateralis (VL), and may be more critical in positions of reduced passive support for the patellofemoral joint (i.e., full extension). Therefore, the aim of this study was to determine whether the degree of motor unit synchronization between the vasti muscles is dependent on joint angle. Electromyographic (EMG) recordings of single motor unit action potentials (MUAPs) were made from VMO and multiunit recordings from VL during isometric contractions of the quadriceps at 0 degrees, 30 degrees, and 60 degrees of knee flexion. The degree of synchronization between motor unit firing was evaluated by identification of peaks in the rectified EMG averages of VL, triggered from MUA-Ps in VMO. The proportion of cases in which there was a significant peak in the triggered averages was calculated. There was no significant difference in the degree of synchronization between the vasti at different knee angles (p = 0.57). These data suggest that this basic coordinative mechanism between the vasti muscles is controlled consistently throughout knee range of motion, and is not augmented at specific angles where the requirement for dynamic control of stability is increased. (D 2006 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

Chaos Theory as an Approach to Understanding MICE in Time of Crisis

MICE (meetings, incentives, conventions, and exhibitions), has generated high foreign exchange revenue for the economy worldwide. In Thailand, MICE tourists are recognized as ‘quality’ visitors, mainly because of their high-spending potential. Having said that, Thailand’s MICE sector has been influenced by a number of crises following September 11, 2001. Consequently, professionals in the MICE sector must be prepared to deal with such complex phenomena of crisis that might happen in the future. While a number of researches have examined the complexity of crises in the tourism context, there has been little focus on such issues in the MICE sector. As chaos theory provides a particularly good model for crisis situations, it is the aim of this paper to propose a chaos theory-based approach to the understanding of complex and chaotic system of the MICE sector in time of crisis.

Towards a unified understanding of event-related changes in the EEG:the Firefly model of synchronization through cross-frequency phase modulation

Although event-related potentials (ERPs) are widely used to study sensory, perceptual and cognitive processes, it remains unknown whether they are phase-locked signals superimposed upon the ongoing electroencephalogram (EEG) or result from phase-alignment of the EEG. Previous attempts to discriminate between these hypotheses have been unsuccessful but here a new test is presented based on the prediction that ERPs generated by phase-alignment will be associated with event-related changes in frequency whereas evoked-ERPs will not. Using empirical mode decomposition (EMD), which allows measurement of narrow-band changes in the EEG without predefining frequency bands, evidence was found for transient frequency slowing in recognition memory ERPs but not in simulated data derived from the evoked model. Furthermore, the timing of phase-alignment was frequency dependent with the earliest alignment occurring at high frequencies. Based on these findings, the Firefly model was developed, which proposes that both evoked and induced power changes derive from frequency-dependent phase-alignment of the ongoing EEG. Simulated data derived from the Firefly model provided a close match with empirical data and the model was able to account for i) the shape and timing of ERPs at different scalp sites, ii) the event-related desynchronization in alpha and synchronization in theta, and iii) changes in the power density spectrum from the pre-stimulus baseline to the post-stimulus period. The Firefly Model, therefore, provides not only a unifying account of event-related changes in the EEG but also a possible mechanism for cross-frequency information processing.

Phase synchronization scheme for a practical phase sensitive amplifier of ASK-NRZ signals

We present a phase locking scheme that enables the demonstration of a practical dual pump degenerate phase sensitive amplifier for 10 Gbit/s non-return to zero amplitude shift keying signals. The scheme makes use of cascaded Mach Zehnder modulators for creating the pump frequencies as well as of injection locking for extracting the signal carrier and synchronizing the local lasers. An in depth optimization study has been performed, based on measured error rate performance, and the main degradation factors have been identified.

Control of spatiotemporal chaos in catalytic CO oxidation by laser-induced pacemakers

Control of spatiotemporal chaos is achieved in the catalytic oxidation of CO on Pt(110) by localized modification of the kinetic properties of the surface chemical reaction. In the experiment, a small temperature heterogeneity is created on the surface by a focused laser beam. This heterogeneity constitutes a pacemaker and starts to emit target waves. These waves slowly entrain the medium and suppress the spatiotemporal chaos that is present in the absence of control. We compare this experimental result with a numerical study of the Krischer-Eiswirth-Ertl model for CO oxidation on Pt(110). We confirm the experimental findings and identify regimes where complete and partial controls are possible.

Suppression of spatiotemporal chaos in the oscillatory CO oxidation on Pt(110) by focused laser light

Chemical turbulence in the oscillatory catalytic CO oxidation on Pt(110) is suppressed by means of focused laser light. The laser locally heats the platinum surface which leads to a local increase of the oscillation frequency, and to the formation of a pacemaker which emits target waves. These waves slowly entrain the medium and suppress the spatiotemporal chaos present in the absence of laser light. Our experimental results are confirmed by a detailed numerical analysis of one- and two-dimensional media using the Krischer-Eiswirth-Ertl model for CO oxidation on Pt110. Different control regimes are identified and the dispersion relation of the system is determined using the pacemaker as an externally tunable wave source.