Synchronizing Spatiotemporal Chaos in Coupled Nonlinear Oscillators

An observer for an occluded reaction-diffusion system with spatially varying parameters

Spatially dependent parameters of a two-component chaotic reaction-diffusion partial differential equation (PDE) model describing ocean ecology are observed by sampling a single species. We estimate the model parameters and the other species in the system by autosynchronization, where quantities of interest are evolved according to misfit between model and observations, to only partially observed data. Our motivating example comes from oceanic ecology as viewed by remote sensing data, but where noisy occluded data are realized in the form of cloud cover. We demonstrate a method to learn a large-scale coupled synchronizing system that represents the spatio-temporal dynamics and apply a network approach to analyze manifold stability.

Fractal analysis and control of the competition model

Lotka–Volterra population competition model plays an important role in mathematical models. In this paper, Julia set of the competition model is introduced by use of the ideas and methods of Julia set in fractal geometry. Then feedback control is taken on the Julia set of the model. And synchronization of two different Julia sets of the model with different parameters is discussed, which makes one Julia set change to be another. The simulation results show the efficacy of these methods.

Compound synchronization of four memristor chaotic oscillator systems and secure communication

In this paper, a novel kind of compound synchronization among four chaotic systems is investigated, where the drive systems have been conceptually divided into two categories: scaling drive systems and base drive systems. Firstly, a sufficient condition is obtained to ensure compound synchronization among four memristor chaotic oscillator systems based on the adaptive technique. Secondly, a secure communication scheme via adaptive compound synchronization of four memristor chaotic oscillator systems is presented. The corresponding theoretical proofs and numerical simulations are given to demonstrate the validity and feasibility of the proposed control technique. The unpredictability of scaling drive systems can additionally enhance the security of communication. The transmitted signals can be split into several parts loaded in the drive systems to improve the reliability of communication.

Transmission projective synchronization of multi-systems with non-delayed and delayed coupling via impulsive control

This paper mainly investigates the transmission projective synchronization of multi systems with non-delayed and delayed coupling via impulsive control. Based on the stability analysis of impulsive differential equation, the control laws and updating laws are designed to realize the transmission projective synchronization. Some criteria and corollaries are derived for the transmission projective synchronization among multi-systems. Numerical examples are presented to verify the effectiveness and correctness of the synchronization within a desired scaling factor. For the multi-systems synchronization model, it seems to have more valuable than the usual one drive system and one response system synchronization model.

The development of generalized synchronization on complex networks

In this paper, we numerically investigate the development of generalized synchronization (GS) on typical complex networks, such as scale-free networks, small-world networks, random networks, and modular networks. By adopting the auxiliary-system approach to networks, we observe that GS generally takes place in oscillator networks with both heterogeneous and homogeneous degree distributions, regardless of whether the coupled chaotic oscillators are identical or nonidentical. We show that several factors, such as the network topology, the local dynamics, and the specific coupling strategies, can affect the development of GS on complex networks.

Hyperlabyrinth chaos: from chaotic walks to spatiotemporal chaos

In this paper we examine a very simple and elegant example of high-dimensional chaos in a coupled array of flows in ring architecture that is cyclically symmetric and can also be viewed as an N-dimensional spatially infinite labyrinth (a "hyperlabyrinth"). The scaling laws of the largest Lyapunov exponent, the Kaplan-Yorke dimension, and the metric entropy are investigated in the high-dimensional limit (3<N<or=101) together with its routes to chaos. It is shown that by tuning the single bifurcation parameter b that governs the dissipation and the number of coupled systems N, the attractor dimension can span the entire range of 0 to N including Hamiltonian (conservative) hyperchaos in the limit of b=0 and, furthermore, spatiotemporal chaotic behavior. Finally, stability analysis reveals interesting and important changes in the dynamics, whether N is even or odd.

Network reorganization driven by temporal interdependence of its elements

We employ an adaptive parameter control technique based on detection of phase/lag synchrony between the elements of the system to dynamically modify the structure of a network of nonidentical, coupled Rossler oscillators. Two processes are simulated: adaptation, under which the initially different properties of the units converge, and rewiring, in which clusters of interconnected elements are formed based on the temporal correlations. We show how those processes lead to different network structures and investigate their optimal characteristics from the point of view of resulting network properties.

Chaotic synchronization through coupling strategies

Usually, complete synchronization (CS) is regarded as the form of synchronization proper of identical chaotic systems, while generalized synchronization (GS) extends CS in nonidentical systems. However, this generally accepted view ignores the role that the coupling plays in determining the type of synchronization. In this work, we show that by choosing appropriate coupling strategies, CS can be observed in coupled chaotic systems with parameter mismatch, and GS can also be achieved in coupled identical systems. Numerical examples are provided to demonstrate these findings. Moreover, experimental verification based on electronic circuits has been carried out to support the numerical results. Our work provides a method to obtain robust CS in synchronization-based chaos communications.

Sporadic feedback control of flow turbulence

In this work we consider the problem of flow turbulence control in a two-dimensional Navier-Stokes equation. We suggest a control strategy which sporadically applies global feedback to a single velocity component of the velocity field. It is found that this control strategy can significantly enhance the control efficiency when the optimal fraction for the control period is suitably chosen, both larger and smaller control time fractions may reduce the control precision. The physical mechanism underlying this interesting and strange behavior is heuristically analyzed, based on mode-mode interactions.

Adaptation through minimization of the phase lag in coupled nonidentical systems

We show that the internal control of adaptation can be obtained from the properties of the phase lag that results from phase synchronization of two nonidentical chaotic oscillators. The direction and magnitude of the phase lag depend upon the relative internal properties of the coupled units, and they can be used as indicators during the adjustment of dynamics, i.e., adaptation of the target unit to match that of the control. The properties of the phase lag are obtained using a method based on the estimation of properties of the distributions of relative event times of both (target and control) units. The phase lag dependent mechanism to control the adaptation process was applied to a system of nonidentical Rössler oscillators and a system of nonidentical Lorenz oscillators. We also elucidate its importance as a control mechanism of the changes of neuronal activity showing its application to neural adaptation.

Local dimension and finite time prediction in spatiotemporal chaotic systems

We show how a recently introduced statistic [Patil et al., Phys. Rev. Lett. 81, 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as having high predictability and vice versa. This conclusion is reached by using methods from dynamical systems theory and Bayesian modeling. In this work we emphasize on the consequences for short time forecasting and examine the relevance for factor analysis. Although we concentrate on coupled map lattices and coupled nonlinear oscillators for convenience, any other spatially distributed system could be used instead, such as turbulent fluid flows.

Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback

We report the first experimental observation of anticipating chaotic synchronization in an optical system using two diode lasers as transmitter and receiver. The transmitter laser is rendered chaotic by application of an optical feedback in an external-cavity configuration. It is found that the anticipation time does not depend on the external-cavity round trip time of the transmitter.

Spatiotemporal communication with synchronized optical chaos

We propose a model system that allows communication of spatiotemporal information using an optical chaotic carrier waveform. The system is based on broad-area nonlinear optical ring cavities, which exhibit spatiotemporal chaos in a wide parameter range. Message recovery is possible through chaotic synchronization between transmitter and receiver. Numerical simulations demonstrate the feasibility of the proposed scheme, and the benefit of the parallelism of information transfer with optical wave fronts.

Phase-frequency synchronization in a chain of periodic oscillators in the presence of noise and harmonic forcings

We study numerically the effects of noise and periodic forcings on cluster synchronization in a chain of Van der Pol oscillators. We generalize the notion of effective synchronization to the case of a spatially extended system. It is shown that the structure of synchronized clusters can be effectively controlled by applying local external forcings. The effect of amplitude relations on the phase dynamics is also explored.

Phase synchronization of coupled ginzburg-landau equations

The occurrence of phase synchronization of a pair of unidirectionally coupled nonidentical Ginzburg-Landau equations is demonstrated and characterized using cyclic and extended phases. Furthermore, it is shown that weak coupling first leads to frequency synchronization and later to phase synchronization. For strong coupling there is evidence for generalized synchronization.

Synchronization and control of coupled ginzburg-landau equations using local coupling

In this paper we discuss the properties of a recently introduced coupling scheme for spatially extended systems based on local spatially averaged coupling signals [see Z. Tasev et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. (to be published); and L. Junge et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2265 (1999)]. Using the Ginzburg-Landau model, we performed an extensive numerical examination of this coupling scheme, i.e., a complete scan through the relevant coupling parameters. Furthermore, we demonstrate suppression and control of spatiotemporal chaos, e.g., stabilizing the homogeneous steady state and spatially localized control. As an application all model parameters of the Ginzburg-Landau equation are estimated given only the local information of the system.

Generation of 1/f noise in locked systems working in nonlinear mode

Properties of the phase fluctuations of a nonlinear oscillator were investigated. The multiscale aspect of synchronization is experimentally confirmed with the observation of lockings at any rational ratio. This global property of synchronization is associated with a local one by the study of the phase locked loop (PLL) under nonlinear conditions. We show that the discontinuity between the locking and the free-run state is characterized by the presence of slow temporal variations that induce a low frequency spectrum. An experimental verification of the increase of fluctuations confirms the classical results, which associate 1/f noise to nonlinearity, autosimilarity and regularity, represented here by the synchronization.

Synchronizing spatiotemporal chaos

We show analytically and numerically that a pair of uni-directionally coupled spatially extended systems can synchronize. For the case of partial differential equations the synchronization can be achieved by applying the scalar driving signals only at finite number of space points. Our approach is very general and can be useful for practical applications since the synchronization is achieved via feeding in the response system only the information from certain (discrete) spatial locations of the drive system. We also stress some open problems in the field of synchronization of spatiotemporal chaos. (c) 1997 American Institute of Physics.