Collective Phase Chaos in the Dynamics of Interacting Oscillator Ensembles

We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is arranged through quadratic nonlinear coupling. We show numerically that in the course of alternating Kuramoto transitions to synchrony and back to asynchrony, the exchange of excitations between two subpopulations proceeds in such a way that their collective phases are governed by an expanding circle map similar to the Bernoulli map. We perform the Lyapunov analysis of the dynamics and discuss finite-size effects.Comment: 19 page

Two Scenarios of Breaking Chaotic Phase Synchronization

Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting oscillators, as in the case of classical synchronization of periodic oscillators. If interacting stochastic oscillators are weakly detuned, the phase coherency of the attractors persists when phase synchronization breaks. Conversely, if the control parameters differ considerably, the chaotic attractor becomes phase-incoherent under the conditions of phase synchronization break.Comment: 8 pages, 7 figure

Self-Emerging and Turbulent Chimeras in Oscillator Chains

We report on a self-emerging chimera state in a homogeneous chain of nonlocally and nonlinearly coupled oscillators. This chimera, i.e. a state with coexisting regions of complete and partial synchrony, emerges via a supercritical bifurcation from a homogeneous state and thus does not require preparation of special initial conditions. We develop a theory of chimera basing on the equations for the local complex order parameter in the Ott-Antonsen approximation. Applying a numerical linear stability analysis, we also describe the instability of the chimera and transition to a phase turbulence with persistent patches of synchrony

Partially integrable dynamics of hierarchical populations of coupled oscillators

We consider oscillator ensembles consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble to a relatively small number of dynamical variables plus constants of motion. This reduction is independent of the sizes of subpopulations and remains valid in the thermodynamic limits. The theory is applied to the standard Kuramoto model and to the description of two interacting subpopulations, where we report a novel, quasiperiodic chimera state.Comment: 4 pages, 1 figur

Optimal Phase Description of Chaotic Oscillators

We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincar\'e surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled of the amplitude dynamics, and provides a proper description of phase resetting of chaotic oscillations. The method is illustrated with the R\"ossler and Lorenz systems.Comment: 10 Pages, 14 Figure

A new model for mixing by double-diffusive convection (semi-convection): I. The conditions for layer formation

The process referred to as "semi-convection" in astrophysics and "double-diffusive convection in the diffusive regime" in Earth and planetary sciences, occurs in stellar and planetary interiors in regions which are stable according to the Ledoux criterion but unstable according to the Schwarzschild criterion. In this series of papers, we analyze the results of an extensive suite of 3D numerical simulations of the process, and ultimately propose a new 1D prescription for heat and compositional transport in this regime which can be used in stellar or planetary structure and evolution models. In a preliminary study of the phenomenon, Rosenblum et al. (2011) showed that, after saturation of the primary instability, a system can evolve in one of two possible ways: the induced turbulence either remains homogeneous, with very weak transport properties, or transitions into a thermo-compositional staircase where the transport rate is much larger (albeit still smaller than in standard convection). In this paper, we show that this dichotomous behavior is a robust property of semi-convection across a wide region of parameter space. We propose a simple semi-analytical criterion to determine whether layer formation is expected or not, and at what rate it proceeds, as a function of the background stratification and of the diffusion parameters (viscosity, thermal diffusivity and compositional diffusivity) only. The theoretical criterion matches the outcome of our numerical simulations very adequately in the numerically accessible "planetary" parameter regime, and can easily be extrapolated to the stellar parameter regime. Subsequent papers will address more specifically the question of quantifying transport in the layered case and in the non-layered case.Comment: Submitted to Ap

Toxic Megacolon in Granulomatous Colitis

Acute, toxic dilatation of the colon in granulomatous colitis occurs more frequently than heretofore reported, and is a more serious complication than its counterpart in ulcerative colitis. Twenty-six patients who had toxic megacolon were seen at the Henry Ford Hospital between 1961 and 1971. Fourteen of these had ulcerative colitis and 12 had granulomatous colitis. Coricosteroids were relatively ineffective in these 12 patients and all but two needed surgical intervention. Postoperative complications occurred in two cases, with two deaths. Although the initial clinical picture between the two conditions is identical, the clinical course In those with granulomatous colitis is more serious. The radiological picture is generally similar, but some differences were appreciated. Distension in granulomatous colitis was generally confined to the transverse colon with a noticeable lack of distension in the sigmoid segment. Inflammatory polyps were invariably present, and these tended to be more numerous and larger than those seen in distended colons in ulcerative colitis. In view of the more serious clinical course and ineffectiveness of medical management, early surgery is recommended in those patients with toxic distension of the colon complicating granulomatous colitis

Lag time and parameter mismatches in synchronization of unidirectionally coupled chaotic external cavity semiconductor lasers

We report an analysis of synchronization between two unidirectionally coupled chaotic external cavity master/slave semiconductor lasers with two characteristic delay times, where the delay time in the coupling is different from the delay time in the coupled systems themselves. We demonstrate for the first time that parameter mismatches in photon decay rates for the master and slave lasers can explain the experimental observation that the lag time is equal to the coupling delay time.Comment: LaTex, 5 pages, submitted to PRE(R

On the Feasibility of Malware Authorship Attribution

There are many occasions in which the security community is interested to discover the authorship of malware binaries, either for digital forensics analysis of malware corpora or for thwarting live threats of malware invasion. Such a discovery of authorship might be possible due to stylistic features inherent to software codes written by human programmers. Existing studies of authorship attribution of general purpose software mainly focus on source code, which is typically based on the style of programs and environment. However, those features critically depend on the availability of the program source code, which is usually not the case when dealing with malware binaries. Such program binaries often do not retain many semantic or stylistic features due to the compilation process. Therefore, authorship attribution in the domain of malware binaries based on features and styles that will survive the compilation process is challenging. This paper provides the state of the art in this literature. Further, we analyze the features involved in those techniques. By using a case study, we identify features that can survive the compilation process. Finally, we analyze existing works on binary authorship attribution and study their applicability to real malware binaries.Comment: FPS 201

Generalized Chaotic Synchronizationin Coupled Ginzburg-Landau Equations

Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling betweenthe systems are analyzed. The largest spatial Lyapunov exponent is proposed as a new characteristic of the state of a distributed system, and its calculation is described for a distributed oscillatory system. Partial generalized synchronization is introduced as a new type of chaotic synchronization in spatially nonuniform distributed systems. The physical mechanisms responsible for the onset of generalized chaotic synchronization in spatially distributed oscillatory systems are elucidated. It is shown that the onset of generalized chaotic synchronization is described by a modified Ginzburg-Landau equation with additional dissipation irrespective of the type of coupling. The effect of noise on the onset of a generalized synchronization regime in coupled distributed systems is analyzed.Comment: 12 page