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PubMed2003

Influence of solitons on the transition to spatiotemporal chaos in coupled map lattices.

We study the transition from laminar to chaotic behavior in deterministic chaotic coupled map lattices and in an extension of the stochastic Domany-Kinzel cellular automaton [E. Domany and W. Kinzel, Phys. Rev. Lett. 53, 311 (1984)]. For the deterministic coupled map lattices, we find evidence that "solitons" can change the nature of the transition: for short soliton lifetimes it is of second order, while for longer but finite lifetimes, it is more reminiscent of a first-order transition. In the second-order regime, the deterministic model behaves like directed percolation with infinitely many absorbing states; we present evidence obtained from the study of bulk properties and the spreading of chaotic seeds in a laminar background. To study the influence of the solitons more specifically, we introduce a soliton including variant of the stochastic Domany-Kinzel cellular automaton. Similar to the deterministic model, we find a transition from second- to first-order behavior due to the solitons, both in a mean-field analysis and in a numerical study of the statistical properties of this stochastic model. Our study illustrates that under the appropriate mapping some deterministic chaotic systems behave like stochastic models; but it is hard to know precisely which degrees of freedom need to be included in such description.

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PubMed2000

From low-dimensional synchronous chaos to high-dimensional desynchronous spatiotemporal chaos in coupled systems

The dynamic behavior of coupled chaotic oscillators is investigated. For small coupling, chaotic state undergoes a transition from a spatially disordered phase to an ordered phase with an orientation symmetry breaking. For large coupling, a transition from full synchronization to partial synchronization with translation symmetry breaking is observed. Two bifurcation branches, one in-phase branch starting from synchronous chaos and the other antiphase branch bifurcated from spatially random chaos, are identified by varying coupling strength epsilon. Hysteresis, bistability, and first-order transitions between these two branches are observed.

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PubMed2002

Mode locking of spatiotemporally periodic orbits in coupled sine circle map lattices.

We study the organization of mode-locked intervals corresponding to the stable spatiotemporally periodic solutions in a lattice of diffusively coupled sine circle maps with periodic boundary conditions. Spatially periodic initial conditions settle down to spatiotemporally periodic solutions over large regions of the parameter space. In the case of synchronized solutions resulting from synchronized initial conditions, the mode-locked intervals have been seen to follow strict Farey ordering in the temporal periods. However, the nature of the organization of the mode-locked intervals corresponding to higher spatiotemporal periods is highly dependent on initial conditions and on system parameters. Farey ordering in the temporal periods is seen at low coupling for mode-locked intervals of all spatial periods. On the other hand, stable spatial period two solutions show an interesting reversal of Farey ordering at high values of coupling. Other spatially periodic solutions show a complete departure from Farey ordering at high coupling. We also examine the issue of completeness of the mode-locked intervals via a calculation of the fractal dimension of the complement of the mode-locked intervals as a function of the coupling epsilon and the nonlinearity parameter K. Our results are consistent with completeness over a range of values for these parameters. Spatiotemporally periodic solutions of the traveling wave type have their own organization in the parameter space. Novel bifurcations to other types of solutions are seen in the mode-locked intervals. We discuss various features of these bifurcations. We also define a set of new variables using which an analytic treatment of the bifurcations along the Omega=0 line is carried out.

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PubMed2001

Spatiotemporal symmetry in rings of coupled biological oscillators of Physarum plasmodial slime mold.

Spatiotemporal patterns in rings of coupled biological oscillators of the plasmodial slime mold, Physarum polycephalum, were investigated by comparing with results analyzed by the symmetric Hopf bifurcation theory based on group theory. In three-, four-, and five-oscillator systems, all types of oscillation modes predicted by the theory were observed including a novel oscillation mode, a half period oscillation, which has not been reported anywhere in practical systems. Our results support the effectiveness of the symmetric Hopf bifurcation theory in practical systems.

Animals↗
PubMed2003

Spatiotemporal stochastic forcing effects in an ensemble consisting of arrays of diffusively coupled Lorenz cells.

Spatiotemporal stochastic forcing of an ensemble system consisting of chaotic Lorenz cells diffusively coupled is analyzed. The nontrivial effects of time and length correlations on the ensemble mean error and spread are studied and the implications to new trends in weather forecast methodologies are discussed. A maximum for the forecast scores is observed to occur for specific values of time and length correlations. This maximum is studied in terms of an interplay between the natural scales occurring in the system and the noise parameters.

Forecasting↗
PubMed2002

Random coupling of chaotic maps leads to spatiotemporal synchronization.

We investigate the spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections. While strictly nearest neighbor coupling never allows spatiotemporal synchronization in our system, randomly rewiring some of those connections stabilizes entire networks at x*, where x* is the strongly unstable fixed point solution of the local chaotic map. In fact, the smallest degree of randomness in spatial connections opens up a window of stability for the synchronized fixed point in coupling parameter space. Further, the coupling epsilon(bifr) at which the onset of spatiotemporal synchronization occurs, scales with the fraction of rewired sites p as a power law, for 0.1<p<1. We also show that the regularizing effect of random connections can be understood from stability analysis of the probabilistic evolution equation for the system, and approximate analytical expressions for the range and epsilon(bifr) are obtained.

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PubMed2003

Synchronization of spatiotemporal patterns in locally coupled excitable media.

The synchronization of two distributed Belousov-Zhabotinsky systems is experimentally and theoretically investigated. Symmetric local coupling of the systems is made possible with the use of a video camera-projector scheme. The spatial disorder of the coupled systems, with random initial configurations of spirals, gradually decreases until a final state is attained, which corresponds to a synchronized state with a single spiral in each system. The experimental observations are confirmed with numerical simulations of two identical Oregonator models with symmetric local coupling, and a systematic study reveals generalized synchronization of spiral waves. Several different types of synchronization attractors are distinguished.

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PubMed2006

Spatiotemporal intermittency and scaling laws in the coupled sine circle map lattice.

We study spatiotemporal intermittency (STI) in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes with STI of both the directed percolation (DP) and non-DP class. STI with synchronized laminar behavior belongs to the DP class. The regimes of non-DP behavior show spatial intermittency (SI), where the temporal behavior of both the laminar and burst regions is regular, and the distribution of laminar lengths scales as a power law. The regular temporal behavior for the bursts seen in these regimes of spatial intermittency can be periodic or quasiperiodic, but the laminar length distributions scale with the same power law, which is distinct from the DP case. STI with traveling wave laminar states also appears in the phase diagram. Solitonlike structures appear in this regime. These are responsible for crossovers with accompanying nonuniversal exponents. The soliton lifetime distributions show power-law scaling in regimes of long average soliton lifetimes, but peak at characteristic scales with a power-law tail in regimes of short average soliton lifetimes. The signatures of each type of intermittent behavior can be found in the dynamical characterizers of the system viz. the eigenvalues of the stability matrix. We discuss the implications of our results for behavior seen in other systems which exhibit spatiotemporal intermittency.

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PubMed2000

Analysis of spatiotemporally periodic behavior in lattices of coupled piecewise monotonic maps.

We study the stability of spatiotemporally periodic orbits in 1-d lattices of piecewise monotonic maps coupled via translationally invariant coupling and periodic boundary conditions. States of such systems have independent spatial and temporal periodicities and their stability can be studied through the analysis of a single, uniquely identified reduced matrix of size kxk when the system size is MxM, for M=kN, a multiple of k. This result applies for arbitrary temporal periods and is valid for all coupled map lattice systems coupled in a translationally invariant manner with stability matrices which are irreducible and non-negative, as in the present case. Our analysis could be useful in the analysis of stability regions and bifurcation behavior in a variety of spatially extended systems.

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PubMed2006

One-way coupling enables noise-mediated spatiotemporal patterns in media of otherwise quiescent multistable elements.

Recent work has demonstrated that undriven and overdamped bistable systems, which are normally quiescent, can oscillate if unidirectionally coupled into arrays with cyclic boundary conditions. Here, we understand such oscillations as corresponding to the propagation of solitonlike waves. Further, in large arrays, we demonstrate how noise and coupling, together, mediate the resulting complex spatiotemporal dynamics.

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PubMed2001

Influence of low intensity noise on assemblies of diffusively coupled chaotic cells.

The effect of time-correlated and white Gaussian noises of low intensity on one-dimensional arrays consisting of diffusively coupled chaotic cells is analyzed. An improvement or worsening of the synchronization between cells of the array driven by low-intensity colored noise is observed for a resonant interval of time correlation values. A comparison between colored and white noise and additive and multiplicative contribution has been carried out investigating the nonlinear cooperative effects of noise strength, correlation time, and coupling strength to control spatiotemporal chaos in coupled arrays of chaotic cells. The possibility to distinguish highly correlated areas of a diffusively coupled network of cells by using low-intensity time correlated noise is discussed. (c) 2001 American Institute of Physics.

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PubMed2000

Spatiotemporal stability of one-way open coupled nonlinear systems

The present paper investigates the spatiotemporal stability of homogeneous solutions in one-way open coupled nonlinear systems. We show that the H(infinity) norm concept, which has been used as an important index in the field of robust control theory, allows us to grasp the mechanism of spatial instability in coupled systems. Spatial instability occurs only when the H(infinity) norm of the transfer function of each site is greater than 1. It is shown that numerical simulations for one-way open coupled double scroll circuits are in good agreement with our theoretical results.

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PubMed2002

Spatiotemporal stability and control of one-way open coupled Lorenz systems.

We investigate the spatiotemporal stability of a homogeneous solution in one-way open coupled Lorenz systems, and suppress the spatial instability in the systems by using the H(infinity) control technique. The suppression is illustrated with numerical simulations. In addition, it is shown that the suppression can be also achieved for one-way ring-type systems.

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PubMed2001

Wave fronts and spatiotemporal chaos in an array of coupled Lorenz oscillators.

The effects of coupling strength and single-cell dynamics (SCD) on spatiotemporal pattern formation are studied in an array of Lorenz oscillators. Different spatiotemporal structures (stationary patterns, propagating wave fronts, short wavelength bifurcation) arise for bistable SCD, and two well differentiated types of spatiotemporal chaos for chaotic SCD (in correspondence with the transition from stationary patterns to propagating fronts). Wave-front propagation in the bistable regime is studied in terms of global bifurcation theory, while a short wavelength pattern region emerges through a pitchfork bifurcation.

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PubMed2001

Phase coupling and synchrony in the spatiotemporal dynamics of muskrat and mink populations across Canada.

Population ecologists have traditionally focused on the patterns and causes of population variation in the temporal domain for which a substantial body of practical analytic techniques have been developed. More recently, numerous studies have documented how populations may fluctuate synchronously over large spatial areas; analyses of such spatially extended time-series have started to provide additional clues regarding the causes of these population fluctuations and explanations for their synchronous occurrence. Here, we report on the development of a phase-based method for identifying coupling between temporally coincident but spatially distributed cyclic time-series, which we apply to the numbers of muskrat and mink recorded at 81 locations across Canada. The analysis reveals remarkable parallel clines in the strength of coupling between proximate populations of both species--declining from west to east--together with a corresponding increase in observed synchrony between these populations the further east they are located.

Animals↗