We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirect... more We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirectional delayed coupling which are subject to the same external forcing. We demonstrate for different paradigms of excitable system that, due to the coupling, the excitability threshold for the slave system is always lower than that for the master. As a consequence the two systems respond to a common external forcing with different response times.
Abstract We propose a variant of the simulated annealing method for optimization in the multivari... more Abstract We propose a variant of the simulated annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the hybrid Monte Carlo algorithm in their generalized version for the proposal of new configurations. We show how this choice can improve upon the performance of simulated annealing methods (mainly when the number of variables is large) by allowing a more effective searching scheme and a faster annealing schedule.
Abstract: We present an exact solution of a one-dimensional Ising chain with both nearest neighbo... more Abstract: We present an exact solution of a one-dimensional Ising chain with both nearest neighbor and random long-range interactions. Not surprisingly, the solution confirms the mean field character of the transition. This solution also predicts the finite-size scaling that we observe in numerical simulations.
In the last few decades we have witnessed a paradigmatic shift regarding the role of fluctuations... more In the last few decades we have witnessed a paradigmatic shift regarding the role of fluctuations, from the equilibrium picture of merely being a N 1/2 perturbation on thermodynamic averages—or triggering at most phase transitions between well defined minima of the free energy 1—to lead a host of new and amazing phenomena in far from equilibrium situations.
It is shown that a recent proposal to give physically meaningful definitions of temperature and p... more It is shown that a recent proposal to give physically meaningful definitions of temperature and pressure within Tsallis formalism for non-extensive thermostatistics leads to expressions which coincide with those obtained by using the standard Boltzmann formalism of statistical mechanics.
We study the regime of anticipated synchronization in unidirectionally coupled model neurons subj... more 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 (ie, predict) the pulses fired by the master neuron. This anticipated synchronization occurs even when the common external forcing is white noise.
Here we study a noise-induced transition when the system is driven by a noise source taken as col... more Here we study a noise-induced transition when the system is driven by a noise source taken as colored and non-Gaussian. We show—using both, a theoretical approximation and numerical simulations—that there is a shift of the transition as the noise departs from the Gaussian behavior. Also, we confirm the reentrance effect found for colored Gaussian noise and show the behavior of the transition line in the phase-like diagram as the noise departs from Gaussianity in the large correlation time limit.
Abstract We consider stochastic dynamic models studied via computer simulation. We review some ba... more Abstract We consider stochastic dynamic models studied via computer simulation. We review some basic results for the voter model which is probably the simplest model of collective behavior. Specifically, we focus on the dynamical effect of who interacts with whom-that is, the consequences of different interaction networks. We also consider R. Axelrod's (1997) model for the dissemination of culture.
The model introduced by Van den Broeck, Parrondo, and Toral [Phys. Rev. Lett. 73, 3395 (1994)]—le... more The model introduced by Van den Broeck, Parrondo, and Toral [Phys. Rev. Lett. 73, 3395 (1994)]—leading to a second-order-like noise-induced nonequilibrium phase transition which shows reentrance as a function of the (multiplicative) noise intensity s—is investigated beyond the white-noise assumption. Through a Markovian approximation and within a mean-field treatment it is found that, in striking contrast with the usual behavior for equilibrium phase transitions, for noise self-correlation time t.
Abstract: We study the effect that the injection of a common source of noise has on the trajector... more Abstract: We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of 1-d maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization.
We present conclusive evidence showing that different sources of diversity, such as those represe... more We present conclusive evidence showing that different sources of diversity, such as those represented by quenched disorder or noise, can induce a resonant collective behavior in an ensemble of coupled bistable or excitable systems. Our analytical and numerical results show that when such systems are subjected to an external subthreshold signal, their response is optimized for an intermediate value of the diversity.
Lattice models are a powerful basic instrument in the study of phase transitions in equilibrium s... more Lattice models are a powerful basic instrument in the study of phase transitions in equilibrium statistical mechanics, as well as in nonequilibrium systems 1. Traditionally, equilibrium phase transitions have been studied in regular lattices, with the critical temperature being a nonuniversal quantity that depends on the particular lattice under consideration, while critical exponents and some amplitude ratios are universal quantities depending only on spatial dimension and some symmetries of the order parameter.
We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the disseminati... more We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural frozen configurations are found not to be stable. This general result is proven rigorously in d 1, where the dynamics is described in terms of a Lyapunov potential. In d 2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate r T 1 induces monocultural configurations, whereas r T 1 sustains disorder.
We study the effect of finite size population in Galam's model Eur. Phys. J. B 25, 403 (2002) of ... more We study the effect of finite size population in Galam's model Eur. Phys. J. B 25, 403 (2002) of minority opinion spreading and introduce neighborhood models that account for local spatial effects. For systems of different sizes N, the time to reach consensus is shown to scale as \lnN in the original version, while the evolution is much slower in the new neighborhood models.
We carry out a systematic study of a different type of chaos at onset ''soft-mode turbulence''bas... more 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.
In many cases, the nucleation of spatio-temporal patterns is associated with continuous symmetry ... more In many cases, the nucleation of spatio-temporal patterns is associated with continuous symmetry breaking, and these patterns are thus very sensitive even to small perturbations or external fields. Perturbations may be induced by imperfections of the system itself eg, impurities, of the geometrical setup eg, the boundary conditions, of the control parameters, etc. In addition, external fields may induce spatial or temporal modulations of the control or bifurcation parameters.
Abstract: The domain growth processes originating from noise-induced nonequilibrium phase transit... more Abstract: The domain growth processes originating from noise-induced nonequilibrium phase transitions are analyzed, both for non-conserved and conserved dynamics. The existence of a dynamical scaling regime is established in the two cases, and the corresponding growth laws are determined. The resulting universal dynamical scaling scenarios are those of Allen-Cahn and Lifshitz-Slyozov, respectively.
The purpose of this paper is to analyze in some detail the arguably simplest case of diversity-in... more The purpose of this paper is to analyze in some detail the arguably simplest case of diversity-induced resonance: that of a system of globally-coupled linear oscillators subjected to a periodic forcing. Diversity appears as the parameters characterizing each oscillator, namely its mass, internal frequency and damping coefficient are drawn from a probability distribution.
We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirect... more We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirectional delayed coupling which are subject to the same external forcing. We demonstrate for different paradigms of excitable system that, due to the coupling, the excitability threshold for the slave system is always lower than that for the master. As a consequence the two systems respond to a common external forcing with different response times.
Abstract We propose a variant of the simulated annealing method for optimization in the multivari... more Abstract We propose a variant of the simulated annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the hybrid Monte Carlo algorithm in their generalized version for the proposal of new configurations. We show how this choice can improve upon the performance of simulated annealing methods (mainly when the number of variables is large) by allowing a more effective searching scheme and a faster annealing schedule.
Abstract: We present an exact solution of a one-dimensional Ising chain with both nearest neighbo... more Abstract: We present an exact solution of a one-dimensional Ising chain with both nearest neighbor and random long-range interactions. Not surprisingly, the solution confirms the mean field character of the transition. This solution also predicts the finite-size scaling that we observe in numerical simulations.
In the last few decades we have witnessed a paradigmatic shift regarding the role of fluctuations... more In the last few decades we have witnessed a paradigmatic shift regarding the role of fluctuations, from the equilibrium picture of merely being a N 1/2 perturbation on thermodynamic averages—or triggering at most phase transitions between well defined minima of the free energy 1—to lead a host of new and amazing phenomena in far from equilibrium situations.
It is shown that a recent proposal to give physically meaningful definitions of temperature and p... more It is shown that a recent proposal to give physically meaningful definitions of temperature and pressure within Tsallis formalism for non-extensive thermostatistics leads to expressions which coincide with those obtained by using the standard Boltzmann formalism of statistical mechanics.
We study the regime of anticipated synchronization in unidirectionally coupled model neurons subj... more 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 (ie, predict) the pulses fired by the master neuron. This anticipated synchronization occurs even when the common external forcing is white noise.
Here we study a noise-induced transition when the system is driven by a noise source taken as col... more Here we study a noise-induced transition when the system is driven by a noise source taken as colored and non-Gaussian. We show—using both, a theoretical approximation and numerical simulations—that there is a shift of the transition as the noise departs from the Gaussian behavior. Also, we confirm the reentrance effect found for colored Gaussian noise and show the behavior of the transition line in the phase-like diagram as the noise departs from Gaussianity in the large correlation time limit.
Abstract We consider stochastic dynamic models studied via computer simulation. We review some ba... more Abstract We consider stochastic dynamic models studied via computer simulation. We review some basic results for the voter model which is probably the simplest model of collective behavior. Specifically, we focus on the dynamical effect of who interacts with whom-that is, the consequences of different interaction networks. We also consider R. Axelrod's (1997) model for the dissemination of culture.
The model introduced by Van den Broeck, Parrondo, and Toral [Phys. Rev. Lett. 73, 3395 (1994)]—le... more The model introduced by Van den Broeck, Parrondo, and Toral [Phys. Rev. Lett. 73, 3395 (1994)]—leading to a second-order-like noise-induced nonequilibrium phase transition which shows reentrance as a function of the (multiplicative) noise intensity s—is investigated beyond the white-noise assumption. Through a Markovian approximation and within a mean-field treatment it is found that, in striking contrast with the usual behavior for equilibrium phase transitions, for noise self-correlation time t.
Abstract: We study the effect that the injection of a common source of noise has on the trajector... more Abstract: We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of 1-d maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization.
We present conclusive evidence showing that different sources of diversity, such as those represe... more We present conclusive evidence showing that different sources of diversity, such as those represented by quenched disorder or noise, can induce a resonant collective behavior in an ensemble of coupled bistable or excitable systems. Our analytical and numerical results show that when such systems are subjected to an external subthreshold signal, their response is optimized for an intermediate value of the diversity.
Lattice models are a powerful basic instrument in the study of phase transitions in equilibrium s... more Lattice models are a powerful basic instrument in the study of phase transitions in equilibrium statistical mechanics, as well as in nonequilibrium systems 1. Traditionally, equilibrium phase transitions have been studied in regular lattices, with the critical temperature being a nonuniversal quantity that depends on the particular lattice under consideration, while critical exponents and some amplitude ratios are universal quantities depending only on spatial dimension and some symmetries of the order parameter.
We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the disseminati... more We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural frozen configurations are found not to be stable. This general result is proven rigorously in d 1, where the dynamics is described in terms of a Lyapunov potential. In d 2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate r T 1 induces monocultural configurations, whereas r T 1 sustains disorder.
We study the effect of finite size population in Galam's model Eur. Phys. J. B 25, 403 (2002) of ... more We study the effect of finite size population in Galam's model Eur. Phys. J. B 25, 403 (2002) of minority opinion spreading and introduce neighborhood models that account for local spatial effects. For systems of different sizes N, the time to reach consensus is shown to scale as \lnN in the original version, while the evolution is much slower in the new neighborhood models.
We carry out a systematic study of a different type of chaos at onset ''soft-mode turbulence''bas... more 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.
In many cases, the nucleation of spatio-temporal patterns is associated with continuous symmetry ... more In many cases, the nucleation of spatio-temporal patterns is associated with continuous symmetry breaking, and these patterns are thus very sensitive even to small perturbations or external fields. Perturbations may be induced by imperfections of the system itself eg, impurities, of the geometrical setup eg, the boundary conditions, of the control parameters, etc. In addition, external fields may induce spatial or temporal modulations of the control or bifurcation parameters.
Abstract: The domain growth processes originating from noise-induced nonequilibrium phase transit... more Abstract: The domain growth processes originating from noise-induced nonequilibrium phase transitions are analyzed, both for non-conserved and conserved dynamics. The existence of a dynamical scaling regime is established in the two cases, and the corresponding growth laws are determined. The resulting universal dynamical scaling scenarios are those of Allen-Cahn and Lifshitz-Slyozov, respectively.
The purpose of this paper is to analyze in some detail the arguably simplest case of diversity-in... more The purpose of this paper is to analyze in some detail the arguably simplest case of diversity-induced resonance: that of a system of globally-coupled linear oscillators subjected to a periodic forcing. Diversity appears as the parameters characterizing each oscillator, namely its mass, internal frequency and damping coefficient are drawn from a probability distribution.
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