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R Toral

Publications and source records attributed to R Toral.

At least 19 recordsLinked to original sources
PubMed2003

Anticipating the response of excitable systems driven by random forcing.

We study the regime of anticipated synchronization in unidirectionally coupled model neurons subject to a common external aperiodic forcing that makes their behavior unpredictable. We show numerically and by analog hardware electronic circuits that, under appropriate coupling conditions, the pulses fired by the slave neuron anticipate (i.e., predict) the pulses fired by the master neuron. This anticipated synchronization occurs even when the common external forcing is white noise.

Action Potentials↗
PubMed2001

Transition from oscillatory to excitable regime in a system forced at three times its natural frequency.

The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from the strong coupling between the external field and the unstable modes. We show that, by increasing the intensity of the forcing, one passes from an oscillatory regime to an excitable one with three equivalent frequency-locked states. In the oscillatory regime, topological defects are one-armed phase spirals, while in the excitable regime they correspond to three-armed excitable amplitude spirals. Analytical results show that the transition between these two regimes occurs at a critical value of the forcing intensity. The transition between phase and amplitude spirals is confirmed by numerical analysis and it might be observed in periodically forced reaction-diffusion systems.

Journal Article↗
PubMed2001

Stochastic effects in intercellular calcium spiking in hepatocytes.

We carry out a Monte Carlo simulation of stochastic effects for two models of intercellular calcium wave propagation in rat hepatocytes. Both models involve gap junction diffusion by a second messenger. We find that, in general, the stochastic effects improve agreement with experiment, for a reasonable choice of model parameters. Both stochastic models exhibit baseline fluctuations and variations in the peak heights of Ca(2+). In addition, we find for one model that there is a distribution of latency times, rather than a single latency time, with a distribution width which is comparable to the experimental observation of spike widths. We also find for the other model with low gap junction diffusion that it is possible for cell multiplets to oscillate independently initially, but to subsequently become synchronized.

Animals↗
PubMed2000

Stochastic spatiotemporal intermittency and noise-induced transition to an absorbing phase

We introduce a stochastic partial differential equation capable of reproducing the main features of spatiotemporal intermittency (STI). The model also displays a noise-induced transition from STI to laminarity as the noise intensity increases. Simulations and mean-field analysis are used to characterize this transition and to give a quantitative prescription of its loci in the relevant parameter space.

Journal Article↗
PubMed2000

Nonequilibrium phase transitions induced by multiplicative noise: effects of self-correlation

A recently introduced lattice model, describing an extended system which exhibits a reentrant (symmetry-breaking, second-order) noise-induced nonequilibrium phase transition, is studied under the assumption that the multiplicative noise leading to the transition is colored. Within an effective Markovian approximation and a mean-field scheme it is found that when the self-correlation time tau of the noise is different from zero, the transition is also reentrant with respect to the spatial coupling D. In other words, at variance with what one expects for equilibrium phase transitions, a large enough value of D favors disorder. Moreover, except for a small region in the parameter subspace determined by the noise intensity sigma and D, an increase in tau usually prevents the formation of an ordered state. These effects are supported by numerical simulations.

Journal Article↗
PubMed2000

Extensive chaos in the nikolaevskii model

We carry out a systematic study of a different type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one-dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter epsilon. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wave numbers and small frequency.

Journal Article↗
PubMed1999

Noise-induced phase separation: mean-field results.

We present a study of a phase-separation process induced by the presence of spatially correlated multiplicative noise. We develop a mean-field approach suitable for conserved-order-parameter systems and use it to obtain the phase diagram of the model. Mean-field results are compared with numerical simulations of the complete model in two dimensions. Additionally, a comparison between the noise-driven dynamics of conserved and nonconserved systems is made at the level of the mean-field approximation.

Journal Article↗