Complex Spatio-temporal Phenomena Research Articles

Quantification of Turbulence in the Belousov−Zhabotinsky Reaction by Monitoring Wave Tips

We analyze experimentally the tip's motion under conditions in which waves are disorderly distorted by “ripples”. We thus reduce a complex spatiotemporal phenomenon to a purely temporal process, which we then quantify by the maximum Lyapunov exponent. In contrast to the periodic or quasiperiodic tip meanderings reported so far, we present evidence for chaotic tip motion in the case of ripples induced by oxygen in the ferroin- and the ruthenium-catalyzed reactions. For ripples induced by light in the ruthenium-catalyzed reaction, we find absence of chaos in the tip; this points to significant mechanistic differences between the action of light and that of oxygen. Our findings are corroborated by the determination of the power spectra. Chaotic meandering is relevant to spiral drift techniques owing to the essential role of the interaction of the spiral tip with external drift-inducing stimuli.

Dynamics of circular arrays of Josephson junctions and the discrete sine-Gordon equation

We analyze the damped, driven, discrete sine-Gordon equation with periodic boundary conditions and constant forcing. Analytical and numerical results are presented about the existence, stability, and bifurcations of traveling waves in this system. These results are compared with experimental measurements of the current-voltage ( I–V) characteristics of a ring of N = 8 underdamped Josephson junctions. We find two types of traveling waves: low-velocity kinks and high-velocity whirling modes. The kinks excite small-amplitude linear waves intheir wake. At certain drive strengths, the linear waves phase-lock to the kink, generating resonant steps in the I–V curve. Steps also occur in the high-velocity region, due to parametric instabilities of the whirling mode. We analyze the onset of these instabilities, then numerically study the secondary bifurcations and complex spatiotemporal phenomena that occur past the onset. In all cases, the measured voltage locations of the resonant steps are in good agreement with the predictions.

Transient 1/f noise.

We provide examples of transient (nonasymptotic) $\frac{1}{f}$ noise, occurring over reasonably long time scales, in extended nonlinear systems modeling complex spatiotemporal phenomena. These studies contribute towards establishing that transient phenomena, which is often quite relevant in numerical and laboratory experiments, can hold a wealth of interesting dynamical features.

Collective Phenomena in Spatially Extended Evolutionary Games

A class of spatially extended evolutionary games with simple local rules is introduced. The emergent properties are studied through two complementary approaches. One is based on a heuristic local analysis, the other on exact global techniques.The local analysis provides criteria to group the games into classes with distinct behavior. The results facilitate numerical simulations and reveal that even simple games allow for complex spatio-temporal phenomena. The global analysis demonstrates that certain games perform an uphill march in a fitness landscape determined by the payoff parameters and the topology of the underlying lattice structure. For generic game parameters, the landscape is rugged owing to competing interactions and generates dynamical phenomena well known from frustrated systems: trapping in local maxima for noiseless dynamics and very long relaxation times for stochastic dynamics.Although the model is a mere caricature of evolutionary processes, some of its emergent properties are reminiscent of those observed in nature. It is argued that similar dynamical phenomena will be present in more elaborate approaches.

Controlling extended systems of chaotic elements.

A control scheme is devised for taming the dynamics of convectively unstable extended systems exhibiting chaotic behavior. We show how complex spatiotemporal phenomena can be eliminated in arrays of coupled chaotic elements, in favor of a coherent state in which all elements are synchronized to a prescribed periodic orbit of the uncoupled system. The propagation of the synchronizing front and the resulting steady state properties of the array are anlayzed in the presence of noise.

An Event-based Spatiotemporal Approach

With the development of temporal GIS (TGIS), users are not satisfied with the traditional static 2-dimensioinal maps any more, for the real-world entities are evolving in both space and time. Many papers have been brought to propose data models and query languages for TGIS applications. However they are not really adapted for the representation of dynamic geographical phenomena. The current concept of version is not suitable for storing continuous entity evolving information. To fulfil this work, this paper discusses the extended concept of version, called dynamic version, for modelling spatiotemporal entity evolution. The new definition of events and processes this paper presented allows for comprehensive decomposition and representation of complex spatiotemporal phenomena. Two application examples of our approach are brought out to discuss how we express temporal relationships among geographical entities and links describing their joint evolution.