Comment on ``Intermittent Synchronization in a Pair of Coupled Chaotic Pendula"

The main aim of this comment is to emphasize that the conditional Lyapunov exponents play an important role in distinguishing between intermittent and persistent synchronization, when the analytic criteria for asymptotic stability are not uniformly obeyed.Comment: 2 pages, RevTeX 4, 1 EPS figur

Enhancing Synchrony in Chaotic Oscillators by Dynamic Relaying

In a chain of mutually coupled oscillators, the coupling threshold for synchronization between the outermost identical oscillators decreases when a type of impurity (in terms of parameter mismatch) is introduced in the inner oscillator(s). The outer oscillators interact indirectly via dynamic relaying, mediated by the inner oscillator(s). We confirm this enhancing of critical coupling in the chaotic regimes of R\"ossler system in absence of coupling delay and in Mackey-Glass system with delay coupling. The enhancing effect is experimentally verified in electronic circuit of R\"ossler oscillators.Comment: 4 pages, 9 figure

On Provably Safe and Live Multirobot Coordination With Online Goal Posting

A standing challenge in multirobot systems is to realize safe and efficient motion planning and coordination methods that are capable of accounting for uncertainties and contingencies. The challenge is rendered harder by the fact that robots may be heterogeneous and that their plans may be posted asynchronously. Most existing approaches require constraints on the infrastructure or unrealistic assumptions on robot models. In this article, we propose a centralized, loosely-coupled supervisory controller that overcomes these limitations. The approach responds to newly posed constraints and uncertainties during trajectory execution, ensuring at all times that planned robot trajectories remain kinodynamically feasible, that the fleet is in a safe state, and that there are no deadlocks or livelocks. This is achieved without the need for hand-coded rules, fixed robot priorities, or environment modification. We formally state all relevant properties of robot behavior in the most general terms possible, without assuming particular robot models or environments, and provide both formal and empirical proof that the proposed fleet control algorithms guarantee safety and liveness

Ensemble averageability in network spectra

The extreme eigenvalues of connectivity matrices govern the influence of the network structure on a number of network dynamical processes. A fundamental open question is whether the eigenvalues of large networks are well represented by ensemble averages. Here we investigate this question explicitly and validate the concept of ensemble averageability in random scale-free networks by showing that the ensemble distributions of extreme eigenvalues converge to peaked distributions as the system size increases. We discuss the significance of this result using synchronization and epidemic spreading as example processes.Comment: 4 pages, 4 figure

A Unified Approach to Attractor Reconstruction

In the analysis of complex, nonlinear time series, scientists in a variety of disciplines have relied on a time delayed embedding of their data, i.e. attractor reconstruction. The process has focused primarily on heuristic and empirical arguments for selection of the key embedding parameters, delay and embedding dimension. This approach has left several long-standing, but common problems unresolved in which the standard approaches produce inferior results or give no guidance at all. We view the current reconstruction process as unnecessarily broken into separate problems. We propose an alternative approach that views the problem of choosing all embedding parameters as being one and the same problem addressable using a single statistical test formulated directly from the reconstruction theorems. This allows for varying time delays appropriate to the data and simultaneously helps decide on embedding dimension. A second new statistic, undersampling, acts as a check against overly long time delays and overly large embedding dimension. Our approach is more flexible than those currently used, but is more directly connected with the mathematical requirements of embedding. In addition, the statistics developed guide the user by allowing optimization and warning when embedding parameters are chosen beyond what the data can support. We demonstrate our approach on uni- and multivariate data, data possessing multiple time scales, and chaotic data. This unified approach resolves all the main issues in attractor reconstruction.Comment: 22 pages, revised version as submitted to CHAOS. Manuscript is currently under review. 4 Figures, 31 reference

Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators

A new behavior type of unidirectionally coupled chaotic oscillators near the generalized synchronization transition has been detected. It has been shown that the generalized synchronization appearance is preceded by the intermitted behavior: close to threshold parameter value the coupled chaotic systems demonstrate the generalized synchronization most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous bursts. This type of the system behavior has been called intermitted generalized synchronization (IGS) by analogy with intermitted lag synchronization (ILS) [Phys. Rev. E \textbf{62}, 7497 (2000)].Comment: 8 pages, 5 figures, using epl.cls; published in Europhysics Letters. 70, 2 (2005) 169-17

Slower Speed and Stronger Coupling: Adaptive Mechanisms of Self-Organized Chaos Synchronization

We show that two initially weakly coupled chaotic systems can achieve self-organized synchronization by adaptively reducing their speed and/or enhancing the coupling strength. Explicit adaptive algorithms for speed-reduction and coupling-enhancement are provided. We apply these algorithms to the self-organized synchronization of two coupled Lorenz systems. It is found that after a long-time self-organized process, the two coupled chaotic systems can achieve synchronization with almost minimum required coupling-speed ratio.Comment: 4 pages, 5 figure

Synchronization of Time-Continuous Chaotic Oscillators

Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded in the fully synchronized state lose their transverse stability, and the appearance of globally and locally riddled basins of attraction is discussed, respectively, in terms of the subcritical, supercritical nature of the riddling bifurcations. We show how the introduction of a small parameter mismatch between the interacting chaotic oscillators causes a shift of the synchronization manifold. The presence of a coupling asymmetry is found to lead to further modifications of the destabilization process. Finally, the paper considers the problem of partial synchronization in a system of four coupled Rössler oscillators

Synchronization Based Approach for Estimating All Model Parameters of Chaotic Systems

The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of noise, enables online estimation of the parameters and is also able to rapidly track changes in operating parameters of the experimental system. The method is demonstrated using the Lorenz, Rossler chaos and hyperchaos models. Its possible application in decoding communications using chaos is discussed.Comment: 13 pages, 4 figure