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Martinez-Garcia R.,IFISC Institute Fisica Interdisciplinar Y Sistemas Complejos | Martinez-Garcia R.,Princeton University | Murgui C.,IFISC Institute Fisica Interdisciplinar Y Sistemas Complejos | Hernandez-Garcia E.,IFISC Institute Fisica Interdisciplinar Y Sistemas Complejos | Lopez C.,IFISC Institute Fisica Interdisciplinar Y Sistemas Complejos
PLoS ONE | Year: 2015

We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological organisms (like mussels) that tend to cluster at short ranges as a defensive strategy, and strongly disperse if there is a high population pressure at large ranges for optimizing foraging. We perform stochastic simulations of a particle-level model of the system, and derive and analyze a continuous density description (a nonlinear diffusion equation). In both cases we show that this interplay of scaledependent- behaviors gives rise to a rich formation of spatial patterns ranging from labyrinths to periodic cluster arrangements. In most cases these clusters have the very peculiar appearance of ring-like structures, i.e., organisms arranging in the perimeter of the clusters, which we discuss in detail. © 2015 Martínez-García et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


Toral R.,IFISC Institute Fisica Interdisciplinar Y Sistemas Complejos
AIP Conference Proceedings | Year: 2011

I will briefly review the field of noise-induced phase transitions, emphasizing the main differences with the phase-induced transitions and showing that they appear in different systems. I will show that a noise-induced transition can disappear after a suitable change of variables and I will also discuss the breaking of ergodicity and symmetry breaking that occur in noise-induced phase transitions in the thermodynamic limit, but not in noise-induced transitions. © 2011 American Institute of Physics.


Van Den Broeck C.,Hasselt University | Toral R.,IFISC Institute Fisica Interdisciplinar y Sistemas Complejos
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2014

We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device. © 2014 American Physical Society.


Ciszak M.,CNR Institute of Neuroscience | Mayol C.,IFISC Institute Fisica Interdisciplinar y Sistemas Complejos | Mirasso C.R.,IFISC Institute Fisica Interdisciplinar y Sistemas Complejos | Toral R.,IFISC Institute Fisica Interdisciplinar y Sistemas Complejos
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2015

We study the occurrence of anticipated synchronization in two complex Ginzburg-Landau systems coupled in a master-slave configuration. Master and slave systems are ruled by the same autonomous function, but the slave system receives the injection from the master and is subject to a negative delayed self-feedback loop. We give evidence that the magnitude of the largest anticipation time, obtained for complex-valued coupling constants, depends on the dynamical regime where the system operates (defect turbulence, phase turbulence, or bichaos) and scales with the linear autocorrelation time of the system. We also provide analytical conditions for the stability of the anticipated synchronization manifold that are in qualitative agreement with those obtained numerically. Finally, we report on the existence of anticipated synchronization in coupled two-dimensional complex Ginzburg-Landau systems. © 2015 American Physical Society.


Lafuerza L.F.,IFISC Institute Fisica Interdisciplinar y Sistemas Complejos | Toral R.,IFISC Institute Fisica Interdisciplinar y Sistemas Complejos
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter them. We also study the effect of distributed delay. We apply the method to a protein-dynamics model that explicitly includes transcription and translation delays. The theoretical model allows us to understand in a general way the interplay between stochasticity and delay. © 2011 American Physical Society.


PubMed | IFISC Institute Fisica Interdisciplinar y Sistemas Complejos and Hasselt University
Type: Journal Article | Journal: Physical review. E, Statistical, nonlinear, and soft matter physics | Year: 2014

We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device.


PubMed | IFISC Institute Fisica Interdisciplinar y Sistemas Complejos
Type: Journal Article | Journal: Interface focus | Year: 2012

Circadian rhythms in mammals are controlled by the neurons located in the suprachiasmatic nucleus of the hypothalamus. In physiological conditions, the system of neurons is very efficiently entrained by the 24 h light-dark cycle. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light-dark cycle in neuronal synchronization. Nevertheless, heterogeneity as a natural and permanent ingredient of these cellular interactions seemingly plays a major role in these biochemical processes. In this paper, we use a model that considers the neurons of the suprachiasmatic nucleus as chemically coupled modified Goodwin oscillators, and introduce non-negligible heterogeneity in the periods of all neurons in the form of quenched noise. The system response to the light-dark cycle periodicity is studied as a function of the interneuronal coupling strength, external forcing amplitude and neuronal heterogeneity. Our results indicate that the right amount of heterogeneity helps the extended system to respond globally in a more coherent way to the external forcing. Our proposed mechanism for neuronal synchronization under external periodic forcing is based on heterogeneity-induced oscillator death, damped oscillators being more entrainable by the external forcing than the self-oscillating neurons with different periods.


PubMed | IFISC Institute Fisica Interdisciplinar y Sistemas Complejos and CNR Institute of Neuroscience
Type: Journal Article | Journal: Physical review. E, Statistical, nonlinear, and soft matter physics | Year: 2015

We study the occurrence of anticipated synchronization in two complex Ginzburg-Landau systems coupled in a master-slave configuration. Master and slave systems are ruled by the same autonomous function, but the slave system receives the injection from the master and is subject to a negative delayed self-feedback loop. We give evidence that the magnitude of the largest anticipation time, obtained for complex-valued coupling constants, depends on the dynamical regime where the system operates (defect turbulence, phase turbulence, or bichaos) and scales with the linear autocorrelation time of the system. We also provide analytical conditions for the stability of the anticipated synchronization manifold that are in qualitative agreement with those obtained numerically. Finally, we report on the existence of anticipated synchronization in coupled two-dimensional complex Ginzburg-Landau systems.

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