Raúl Toral

Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop

We characterize the chaotic dynamics of semiconductor lasers subject to either optical or electrooptical feedback modeled by Lang-Kobayashi and Ikeda equations, respectively. This characterization is relevant for secure optical communications based on chaos encryption. In particular, for each system we compute as a function of tunable parameters the Lyapunov spectrum, Kaplan-Yorke dimension and Kolmogorov-Sinai entropy.

Stochastic Numerical Methods: An Introduction for Students and Scientists

1. Review of Probability Concepts 2. Monte Carlo Integration 3. Generation of Non-uniform Random Numbers: Non-correlated Values 4. Dynamical Methods 5. Applications to Statistical Mechanics 6. Introduction to Stochastic Processes 7. Numerical Simulation of Stochastic Differential equations 8.Introduction to Master Equations 9. Numerical Simulations of Master Equations 10. Hybrid Monte Carlo 11. Stochastic Partial Differential Equations A. Generation of Uniform ^U (0 1) Random Numbers B. Generation of n-dimensional Correlated Gaussian Variables C. Calculation of the Correlation Function of a Series D. Collective Algorithms for Spin Systems E. Histogram Extrapolation F. Multicanonical Simulations G. Discrete Fourier Transform

STOCHASTIC RESONANCE IN BISTABLE AND EXCITABLE SYSTEMS: EFFECT OF NON-GAUSSIAN NOISES

We analyze stochastic resonance in systems driven by non-Gaussian noises. For the bistable double well we compare the signal-to-noise ratio resulting from numerical simulations with some quasi-analytical results predicted by a consistent Markovian approximation in the case of a colored non-Gaussian noise. We also study the FitzHugh–Nagumo excitable system in the presence of the same noise. In both systems, we find that, as the noise departs from Gaussian behavior, there is a regime (different for the excitable and the bistable systems) in which there is a notable robustness against noise tuning since the signal-to-noise ratio curve broadens and becomes less sensitive to the actual value of the noise intensity. We also compare our results with some experiments in sensory systems.

Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delay feedback loop

We characterize the chaotic dynamics of semiconductor lasers subject to either optical or electro-optical feedback modeled by Lang-Kobayashi and Ikeda equations, respectively. This characterization is relevant for secure optical communications based on chaos encryption. In particular, for each system we compute as function of tunable parameters the Lyapunov spectrum, Kaplan-Yorke dimension and Kolmogorov-Sinai entropy.

Truels, or Survival of the Weakest

A duel is simply a game with two players, each having a probability of winning that game and each having an intrinsic marksmanship, or ability, associated with his or her performance. The mathematical treatment of this game confirms our simple expectations. If more than two players participate, a series of duels might be needed to determine the absolute winner. This is the case in sports tournaments, which pair teams in all possible ways until the ultimate winner emerges. A truel is a generalization of a duel involving three players and slightly different rules

On the Gaussian Approximation for Master Equations

We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen’s expansion approach (the fact that the probability distribution is Gaussian at first order). We analyze the scaling of the error with a large parameter of the system and compare it with van Kampen’s method. Our theoretical analysis and the study of several examples shows that the Gaussian approximation turns out to be more accurate than van Kampen’s expansion at first order. This could be specially important for problems involving stochastic processes in systems with a small number of particles.

Resonance Induced by Repulsive Links

In nonlinear systems, the right amount of noise can amplify the response to a weak periodic signal, by a phenomenon known as stochastic resonance [1]. It was shown that the same constructive role can be played by any source of disorder [2]. We study an Ising model in a network with disorder induced by the presence of both attractive and repulsive links. The system is subjected to a sub-threshold periodic signal, and the goal is to see how the response is enhanced for a given fraction of repulsive links. This can model a network of spinlike neurons with excitatory and inhibitory couplings. By means of numerical simulations, we find that there is an optimal probability of repulsive links, such that the coherent response is maximal, and we propose a mechanism to explain this resonance.