Scaling and universality in transition to synchronous chaos with local-global interactions

Gade, Prashant M.; Hu, Chin‐Kun

doi:10.1103/physreve.73.036212

Cited by 30 publications

(17 citation statements)

References 54 publications

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“…Usually the Lyapunov approach was able to locate γ c within a precision of 1 − 2 × 10 −4 or even better. In the present case, to simplify the analysis we keep the parameter q = 4 and we analyze system sizes ranging from L = 2 19 to L = 2 23 . The results for the exponents θ and β are shown in Fig.…”

Section: B Continuous Mapsmentioning

confidence: 99%

Chaotic synchronizations of spatially extended systems as nonequilibrium phase transitions

Cencini

Tessone

Torcini

2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via power-law coupling is considered. The synchronization transition is studied as a non-equilibrium phase transition, and its critical properties are analyzed at varying the spatial interaction range as well as the nonlinearity of the dynamical units composing each system. In particular, continuous and discontinuous local maps are considered. In both cases the transitions are of the second order with critical indexes varying with the exponent characterizing the interaction range. For discontinuous maps it is numerically shown that the transition belongs to the anomalous directed percolation (ADP) family of universality classes, previously identified for Lévy-flight spreading of epidemic processes. For continuous maps, the critical exponents are different from those characterizing ADP, but apart from the nearest-neighbor case, the identification of the corresponding universality classes remains an open problem. Finally, to test the influence of deterministic correlations for the studied synchronization transitions, the chaotic dynamical evolutions are substituted by suitable stochastic models. In this framework and for the discontinuous case, it is possible to derive an effective Langevin description that corresponds to that proposed for ADP.

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Section: B Continuous Mapsmentioning

confidence: 99%

Chaotic synchronizations of spatially extended systems as nonequilibrium phase transitions

Cencini

Tessone

Torcini

2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Gade and Hu generalized this definition and defined majority persistence for transition to chaotic synchronization in coupled maps with local-global couplings [16]. Similarly, there is a need to generalize this definition for the logistic map.…”

Section: Introductionmentioning

confidence: 99%

Universal persistence exponent in transition to antiferromagnetic order in coupled logistic maps

Gade

Sahasrabudhe²

2013

Phys. Rev. E

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We study coupled logistic maps on a one-dimensional lattice. We coarse grain the system by labeling the local state + if the value of the variable is above the fixed point and - if the value is below the (nonzero) fixed point, x(*)=1-1/μ. We find that the system exhibits a transition from a global state, in which moving defects occur, to a global state, which is frozen in time (modulo-2). All such states display nonzero value of persistence. Besides, we also observe a state which displays long-range antiferromagnetic order. Onset of such a state is accompanied with a power-law behavior of persistence P(t) as a function of time at the critical line. Usually, persistence transitions show nonuniversal exponent. However, here persistence exponent for synchronous dynamics is 3/8 over the entire lower critical curve. This exponent is the same as one observed for asynchronous Glauber dynamics simulation of zero-temperature Ising model in one dimension. The expected value for synchronous dynamics is 3/4. We present a plausible argument for this scaling.

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“…For example, it has been found that critical behaviors of Ising-type spin models 2) and lattice hard-core particle models 3) can be understood from percolation transitions of properly defined clusters of the systems as in the case of random percolation models, 4) that many percolation models 5) or the Ising model 6) on different lattices has universal finitesize scaling functions, 7) and that transitions to synchronous chaos of the coupled-map lattice model 8) with both local and global couplings have nice universal and scaling behaviors. 9) We have used molecular dynamics (MD) simulations to study relaxation processes in various systems of polymer chains and Lennard-Jones (L-J) molecules; two neighboring monomers along a polymer chain are connected by a rigid bond 10) or a spring of strength k spring . 11) We find that the velocity distributions of monomers in a wide range of simulation time can be well described by Tsallis q-statistics 14), 15) and a single scaling function, where q ≥ 1 and q-statistics becomes the Maxwell-Boltzmann distribution when q → 1.…”

Section: §1 Introductionmentioning

confidence: 99%

Molecular Dynamics Approach to Relaxation and Aggregation of Polymer Chains

2010

Prog. Theor. Phys. Suppl.

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We have used molecular dynamics to simulate various systems of polymer chains and Lennard-Jones molecules; the neighboring monomers along a polymer chain are connected by rigid bonds or spring of strength k spring . We find that the velocity distributions of monomers in a wide range of simulation time can be well described by Tsallis q-statistics [C. Tsallis, J. Stat. Phys. 52 (1988), 479] (q ≥ 1) and a single scaling function; the value of q is related to the conformation constraining potential, the interactions with background fluid, the destruction of chain homogeneity or the value of k spring ; when q → 1, the velocity distribution of monomers becomes Maxwell-Boltzmann distribution. We also find that the polymer chains tend to aggregate as neighboring monomers of a polymer chain have small or zero bending-angle and torsion-angle dependent potentials. The implication of our results for the aggregation of proteins is discussed.

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Scaling and universality in transition to synchronous chaos with local-global interactions

Cited by 30 publications

References 54 publications

Chaotic synchronizations of spatially extended systems as nonequilibrium phase transitions

Chaotic synchronizations of spatially extended systems as nonequilibrium phase transitions

Universal persistence exponent in transition to antiferromagnetic order in coupled logistic maps

Molecular Dynamics Approach to Relaxation and Aggregation of Polymer Chains

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