J. Escalona

Vortices and domain walls in a Chern-Simons theory with magnetic moment interactions

We study the structure and properties of vortices in a recently proposed Abelian Maxwell-Chern-Simons model in

Interaction of noise with excitable dynamics

2+1

GLOBALLY COUPLED MAPS WITH SEQUENTIAL UPDATING

dimensions. The model which is described by a gauge field interacting with a complex scalar field includes two parity- and time-violating terms: the Chern-Simons and the anomalous magnetic terms. Self-dual relativistic vortices are discussed in detail. We also find one-dimensional soliton solutions of the domain wall type. The vortices are correctly described by the domain wall solutions in the large flux limit.

On the estimation of phase synchronization, spurious synchronization and filtering

In this paper, the interaction of noise with excitable dynamics of a three-electrode electrochemical cell is examined. Different scenarios involving both external and internal noise sources are considered. In the case of external noise, aperiodic stochastic resonance and regulation of the noise-induced spiking behaviour are investigated. In the case of internal noise, the interaction of intrinsic electrochemical noise with autonomous nonlinear dynamics is studied. The amplitude of this internal noise, determined by the concentration of chloride ions, is monotonically increased and the provoked dynamics are analysed. Our results indicate that internal noise, similar to its external counterpart, is able to induce regularity in the system response.

Entrainment, Arnold tongues, and duality in a periodically driven integrate-and-fire model

Abstract A system of globally coupled logistic maps with sequential updating is analyzed numerically. It is found that deterministic asynchronous updating schemes may have dramatic influences on the dynamical behaviors of globally coupled systems. Transitions from spatio–temporal chaos to spatially organized states are observed as the coupling parameter varies. It is shown that the model system may exhibit a variety of collective properties such as the clustering, traveling wave patterns, and spatial bifurcation cascades.

Alternating chaotic and periodic dynamics in Chern–Simons–Higgs theory with scalar magnetic interaction

Phase synchronization, viz., the adjustment of instantaneous frequencies of two interacting self-sustained nonlinear oscillators, is frequently used for the detection of a possible interrelationship between empirical data recordings. In this context, the proper estimation of the instantaneous phase from a time series is a crucial aspect. The probability that numerical estimates provide a physically relevant meaning depends sensitively on the shape of its power spectral density. For this purpose, the power spectrum should be narrow banded possessing only one prominent peak [M. Chavez et al., J. Neurosci. Methods 154, 149 (2006)]. If this condition is not fulfilled, band-pass filtering seems to be the adequate technique in order to pre-process data for a posterior synchronization analysis. However, it was reported that band-pass filtering might induce spurious synchronization [L. Xu et al., Phys. Rev. E 73, 065201(R), (2006); J. Sun et al., Phys. Rev. E 77, 046213 (2008); and J. Wang and Z. Liu, EPL 102, 10003 (2013)], a statement that without further specification causes uncertainty over all measures that aim to quantify phase synchronization of broadband field data. We show by using signals derived from different test frameworks that appropriate filtering does not induce spurious synchronization. Instead, filtering in the time domain tends to wash out existent phase interrelations between signals. Furthermore, we show that measures derived for the estimation of phase synchronization like the mean phase coherence are also useful for the detection of interrelations between time series, which are not necessarily derived from coupled self-sustained nonlinear oscillators.

Non‐Abelian Chern‐Simons vortices

Abstract We have studied an integrate-and-fire model neuron driven by a periodic sequence of Gaussian-shaped current pulses of width 1/2N and amplitude e. For large N the current is a sequence of delta pulses and for smaller N it approaches a sine. When N is large, the firing rate f vs. e curve is a staircase of entrainment steps yielding an Arnold tongue structure in the τ vs. e plane. In the small N limit we find novel entrainment steps in the f vs. τ plane, without Arnold tongue structure. The steps in the two N regimes are related by a duality transformation. In the presence of noise in the pulse arrival times, the steps disappear above a critical noise value.

Liénard-Wiechert potentials of a non-Abelian charge

The dynamical behavior of a Chern-Simons-Higgs system is studied for the spatially homogeneous case. The model, described by interacting gauge and scalar fields includes two parity and time violating terms: the Chern-Simons and the scalar magnetic interaction. For the pure Chern-Simons part of the theory the equations of motion are integrable. In general, however, the model system exhibits an interesting pattern of chaos to order transitions as the scalar magnetic moment is varied. The system dynamics are analyzed using a combination of standard techniques, such as phase space portraits, Lyapunov exponents, and Fourier spectra. (c) 2000 American Institute of Physics.

Noise-aided synchronization of coupled chaotic electrochemical oscillators

We study a non‐Abelian Chern‐Simons gauge theory in 2+1 dimensions with an anomalous magnetic coupling to the scalar field. It is shown that for a Φ2 scalar potential the vortex satisfies a set of Bogomol’nyi‐type or self‐duality equations.

Phase-flip transition in coupled electrochemical cells

SummaryThe problem of color and energy radiation from a moving non-Abelian point charge is discussed using the null coordinates formalism. Two different solutions are found. The first one, valid forSU(n) groups, produces no energy radiation as a result of the internal dynamics. For the second solution there is a relation between the internal degrees of freedom and the dynamics of the particle in Minkowski’s space-time; this implies a transfer of energy due to the time evolution in the internal space. Color radiation is discussed for the two solutions.