Geometric signature of complex synchronisation scenarios

Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled systems including different types of synchronisation such as phase, lag, generalised, or even complete synchronisation. Here, we study the geometric signatures of coupling along with the onset of generalised synchronisation between two coupled chaotic oscillators by mapping the systems' individual as well as joint recurrences in phase space to a complex network. For a paradigmatic continuous-time model system, the transitivity properties of the resulting joint recurrence networks display distinct variations associated with changes in the structural similarity between different parts of the considered trajectories. They therefore provide a useful indicator for the emergence of generalised synchronisation. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots by Eckmann et al. (Europhys. Lett. 4 (1987), 973).Comment: 7 pages, 3 figure

A detection theoretical approach to digital communications using autoregressive process shift keying

I klassisk digital kommunikasjon overføres en bitstrøm gjennom en kanal ved å modulere parametrene til en deterministisk bærebølge. Noen kjente eksempler er amplitudemodulasjon (AM), frekvensmodulasjon (FM) og fasemodulasjon (PM). Mottakeren estimerer parametrene til det informasjonsbærende signalet og bruker en deteksjonsregel til å klassifisere den mottatte bølgeformen som en av flere mulige parametriske signaler. Konvensjonelle metoder gir ingen beskyttelse mot at ikke-autoriserte mottakere avlytter og dekoder signalet. Blant ferske metoder som tilbyr en viss beskyttelse mot avlytting finner vi såkalte spredt spektrum-teknikker og kaotiske digitale kodere. Slike teknikker krever nøyakig synkronisering mellom sender og mottaker. Selv små synkroniseringsfeil kan føre til store bitfeilrater hos mottakeren. Denne oppgaven har undersøkt et nytt konsept innen digital kommunikasjon, som er basert på å bruke realisasjoner av stokastiske prosesser som informasjonsbærende signaler. Teknikken har innebygd sikkerhet mot avlytting. Samtidig er det mulig å konstruere dekodere som er enklere enn de som brukes i spredt spektrum og kaotisk kommunikasjon. Målet med prosjektet er å undersøke noen fundamentale egenskaper ved den nye teknikken: 1) Hvordan kan vi finne et statistisk mål på avstand mellom de informasjonsbærende stokastiske prosessene? 2) Hvilken detektor skal vi bruke for å dekode informasjonssekvensen, og hvor god ytelse gir denne? 3) Hvordan skal vi velge de stokastiske prosessene

Asynchronous iterations with flexible communication: contracting operators

AbstractThe concept of flexible communication permits one to model efficient asynchronous iterations on parallel computers. This concept is particularly useful in two practical situations. Firstly, when communications are requested while a processor has completed the current update only partly, and secondly, in the context of inner/outer iterations, when processors are also allowed to make use of intermediate results obtained during the inner iteration in other processors.In the general case of nonlinear or linear fixed point problems, we give a global convergence results for asynchronous iterations with flexible communication whereby the iteration operators satisfy certain contraction hypotheses. In this manner we extend to a contraction context previous results obtained for monotone operators with respect to a partial ordering

Robust output stabilization: improving performance via supervisory control

We analyze robust stability, in an input-output sense, of switched stable systems. The primary goal (and contribution) of this paper is to design switching strategies to guarantee that input-output stable systems remain so under switching. We propose two types of {\em supervisors}: dwell-time and hysteresis based. While our results are stated as tools of analysis they serve a clear purpose in design: to improve performance. In that respect, we illustrate the utility of our findings by concisely addressing a problem of observer design for Lur'e-type systems; in particular, we design a hybrid observer that ensures ``fast'' convergence with ``low'' overshoots. As a second application of our main results we use hybrid control in the context of synchronization of chaotic oscillators with the goal of reducing control effort; an originality of the hybrid control in this context with respect to other contributions in the area is that it exploits the structure and chaotic behavior (boundedness of solutions) of Lorenz oscillators.Comment: Short version submitted to IEEE TA