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In natural systems, many processes can be represented as the result of the interaction of self-sustained oscillators on top of complex topological wirings of connections. We review some of the main results on the setting of collective (synchronized) behaviors in globally and locally identical coupled oscillators, and then discuss in more detail the main formalism that gives the necessary condition for the stability of a synchronous motion. Finally, we also briefly describe a case of a growing network of nonidentical oscillators, where the growth process is entirely guided by dynamical rules, and where the final synchronized state is accompanied with the emergence of a specific statistical feature (the scale-free property) in the network's degree distribution. [ABSTRACT FROM AUTHOR]

The response of a random and modular network to the simultaneous presence of two frequencies is considered. The competition for controlling the dynamics of the network results in different behaviors, such as frequency changes or permanent synchronization frustration, which can be directly related to the network structure. From these observations, we propose a new method for detecting overlapping communities in structured networks. [ABSTRACT FROM AUTHOR]

We introduce the concept of decision cost of a spatial graph, which measures the disorder of a given network taking into account not only the connections between nodes but their position in a two-dimensional map. The influence of the network size is evaluated and we show that normalization of the decision cost allows us to compare the degree of disorder of networks of different sizes. Under this framework, we measure the disorder of the connections between airports of two different countries and obtain some conclusions about which of them is more disordered. The introduced concepts (decision cost and disorder of spatial networks) can easily be extended to Euclidean networks of higher dimensions, and also to networks whose nodes have a certain fitness property (i.e., one-dimensional). [ABSTRACT FROM AUTHOR]

We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler (in the funnel and no funnel regimes), Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled. The main result of the numerical simulations is that in all cases, specific values of coupling strength and asymmetry exist that render the two oscillators periodic and synchronized. The values of the coupling strength for which this phenomenon occurs is well below the previously known value for complete synchronization. We have found that this behavior exists for all the chaotic oscillators that we have used in the analysis. We postulate that this behavior is presumably generic to all chaotic oscillators. In order to complete the study, we have tested the robustness of this phenomenon of chaos suppression versus the addition of some Gaussian noise. We found that chaos suppression is robust for the addition of finite noise level. Finally, we propose some extension to this research. [ABSTRACT FROM AUTHOR]

We propose a method for determining the range of the coupling parameter for which the network of slightly nonidentical chaotic oscillators demonstrates stable synchronous behavior. As an example of using this method, we study the complete-synchronization regime of a network of nonidentical Rossler oscillators. [ABSTRACT FROM AUTHOR]

The conditions for the existence of heteroclinic connections between the transverse modes of a CO2 laser whose setup has a perfect cylindrical symmetry are discussed by symmetry arguments for the cases of three, four and five interacting modes. Explicit conditions for the parameters are derived, which can guide observation of such phenomena. [ABSTRACT FROM AUTHOR]

We numerically investigate the dynamics of a closed chain of unidirectionally coupled oscillators in a regime of homoclinic chaos. The emerging synchronization regimes show analogies with the experimental behavior of a single chaotic laser subjected to a delayed feedback. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Focuses on the transient dynamics of a spiking homoclinic chaotic laser. Deterministic properties of chaotic dynamical systems; Usage of homoclinic chaotic laser to encode discrete sources of information.

We present a simple method for real-time encoding of information in the interspike intervals of a homoclinic chaotic system. The method has been experimentally tested on a CO[sub 2] laser with feedback displaying Sil'nikov chaos and synchronized with an external pulsed signal. Information is encoded by the length of the temporal intervals between consecutive pulses of the external signal. This length is varied each time a new pulse is generated. [ABSTRACT FROM AUTHOR]

The intermittent lag synchronization of two nonidentical symmetrically coupled Rössler systems is investigated numerically. This phenomenon orginates by intermittent bursts away from a principal lag synchronization regime, that correspond to jumps of the system toward other lag configurations. The global scenario of transitions toward a perfect lag synchronization regime may be tracked by the identification of the different lag configurations and the measure of the fraction of time spent by the system in each one of them. The statistical properties of this intermittent behavior are described and compared with the ones of on-off intermittency. [ABSTRACT FROM AUTHOR]

We characterize the synchronization of two nonidentical spatially extended fields ruled by onedimensional Complex Ginzburg-Landau equations, in the two regimes of phase and amplitude turbulence. If two fields display the same dynamical regime, the coupling induces a transition to a completely synchronized state. When, instead, the two fields are in different dynamical regimes, the transition to complete synchronization is mediated by defect synchronization. In the former case, the synchronized manifold is dynamically equivalent to that of the unsynchronized systems, while in the latter case the synchronized state substantially differs from the unsynchronized one, and it is mainly dictated by the synchronization process of the space-time defects. [ABSTRACT FROM AUTHOR]

We describe the emergence of phase clustering and collective behaviors in an ensemble of chaotic coupled map lattices, due to a mean field interaction. This kind of interaction is responsible for the appearence of a collective state, wherein the mean field evolution of each lattice undergoes a periodic behavior in space. We analyze the transition to such a state in an ensemble of one-dimensional lattices of logistic maps, showing that the resulting behavior cooperatively maximizes the energy of the mean field activity. [ABSTRACT FROM AUTHOR]

Introduces an adaptive recognition method consisting in a sequence of variable resolution observation intervals at which the geometrical positions are sampled. Application to a chaotic time series; Synchronization of three chaotic systems; Filtering noise from chaos; Control of chaos.

No abstract received. [ABSTRACT FROM AUTHOR]

© 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper describes the effects of an asymmetric coupling in the synchronization of two spatially extended systems. Namely, we report the consequences induced by the presence of asymmetries in the coupling configuration of a pair of one-dimensional fields obeying Complex Ginzburg–Landau equations. While synchronization always occurs for large enough coupling strengths, asymmetries have the effect of enhancing synchronization and play a crucial role in setting the threshold for the appearance of the synchronized dynamics, as well as in selecting the statistical and dynamical properties of the synchronized motion. We discuss the process of synchronization in the presence of asymmetries by using some analytic expansions valid for a regime of soft spatial temporal chaos (i.e. phase turbulence regime). The influence of phase singularities that break the validity of the analysis is also discussed. [ABSTRACT FROM AUTHOR]

A chaotic system can be guided by tiny perturbations to follow a previously chosen path in phase space carrying a desired sequence of binary symbols. We discuss how to exploit redundancy and flexibility of the chaotic carriers to reconstruct possible signal dropouts incurred in the communication channel, even in the case in which the receiver has no information about the chaotic system on which the message is coded. A crucial issue is whether the natural evolution of the selected chaotic system displays prohibited sequences. We show how to optimize the message recovering process, and how this last one is strictly related to the natural properties of the chaotic sources. [ABSTRACT FROM AUTHOR]

We report on the spontaneous emergence of computation from adaptive synchronization of networked dynamical systems. The fundamentals are nonlinear elements, interacting in a directed graph via a coupling that adapts itself to the synchronization level between two input signals. These units can emulate different Boolean logics, and perform any computational task in a Turing sense, each specific operation being associated with a given network's motif. The resilience of the computation against noise is proven, and the general applicability is demonstrated with regard to periodic and chaotic oscillators, and excitable systems mimicking neural dynamics. [ABSTRACT FROM AUTHOR]