Inés P. Mariño

Phase control of excitable systems

Here we study how to control the dynamics of excitable systems by using the phase control technique. Excitable systems are relevant in neuronal dynamics and therefore this method might have important applications. We use the periodically driven FitzHugh–Nagumo (FHN) model, which displays both spiking and non-spiking behaviours in chaotic or periodic regimes. The phase control technique consists of applying a harmonic perturbation with a suitable phase that we adjust in search of different behaviours of the FHN dynamics. We compare our numerical results with experimental measurements performed on an electronic circuit and find good agreement between them. This method might be useful for a better understanding of excitable systems and different phenomena in neuronal dynamics.

Channel coding in communications using chaos

Abstract We introduce a novel chaotic channel code with error-correcting capabilities. This channel code takes advantage of the natural redundancy contained in the perturbations applied to a chaotic system, in order to encode a desired message in the symbolic dynamics of the chaotic waveform.

Synchronization of uncoupled excitable systems induced by white and coloured noise

We study, both numerically and experimentally, the synchronization of uncoupled excitable systems due to a common noise. We consider two identical FitzHugh–Nagumo systems, which display both spiking and non-spiking behaviours in chaotic or periodic regimes. An electronic circuit provides a laboratory implementation of these dynamics. Synchronization is tested with both white and coloured noise, showing that coloured noise is more effective in inducing synchronization of the systems. We also study the effects on the synchronization of parameter mismatch and of the presence of intrinsic (not common) noise, and we conclude that the best performance of coloured noise is robust under these distortions.

A novel channel coding scheme based on continuous-time chaotic dynamics

One of the most outstanding properties of chaotic dynamical systems is their extreme sensitivity to small perturbations. Far from being a disadvantage, this feature can be exploited to devise a simple technique that allows to control the symbolic dynamics of a chaotic system by applying small perturbations to the system trajectory. In this paper, we show how this procedure can be employed to differentially encode an arbitrary binary message within a continuous-time chaotic waveform generated by a chaotic system. This chaotic waveform is an information-bearing signal that naturally presents a high degree of redundancy. By exploiting this property, we introduce a novel chaotic channel code with error-correcting capabilities.

Parameter Estimation Methods for Chaotic Intercellular Networks

We have investigated simulation-based techniques for parameter estimation in chaotic intercellular networks. The proposed methodology combines a synchronization–based framework for parameter estimation in coupled chaotic systems with some state–of–the–art computational inference methods borrowed from the field of computational statistics. The first method is a stochastic optimization algorithm, known as accelerated random search method, and the other two techniques are based on approximate Bayesian computation. The latter is a general methodology for non–parametric inference that can be applied to practically any system of interest. The first method based on approximate Bayesian computation is a Markov Chain Monte Carlo scheme that generates a series of random parameter realizations for which a low synchronization error is guaranteed. We show that accurate parameter estimates can be obtained by averaging over these realizations. The second ABC–based technique is a Sequential Monte Carlo scheme. The algorithm generates a sequence of “populations”, i.e., sets of randomly generated parameter values, where the members of a certain population attain a synchronization error that is lesser than the error attained by members of the previous population. Again, we show that accurate estimates can be obtained by averaging over the parameter values in the last population of the sequence. We have analysed how effective these methods are from a computational perspective. For the numerical simulations we have considered a network that consists of two modified repressilators with identical parameters, coupled by the fast diffusion of the autoinducer across the cell membranes.

Controlling chaos in a fluid flow past a movable cylinder

Abstract The model of a two-dimensional fluid flow past a cylinder is a relatively simple problem with a strong impact in many applied fields, such as aerodynamics or chemical sciences, although most of the involved physical mechanisms are not yet well known. This paper analyzes the fluid flow past a cylinder in a laminar regime with Reynolds number, Re , around 200, where two vortices appear behind the cylinder, by using an appropriate time-dependent stream function and applying non-linear dynamics techniques. The goal of the paper is to analyze under which circumstances the chaoticity in the wake of the cylinder might be modified, or even suppressed. And this has been achieved with the help of some indicators of the complexity of the trajectories for the cases of a rotating cylinder and an oscillating cylinder.

Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models

The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed {\it nonlinear} population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples,

Basin boundary metamorphoses and phase control

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Comparison of Longitudinal CA125 Algorithms as a First-Line Screen for Ovarian Cancer in the General Population

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A nonlinear population Monte Carlo scheme for Bayesian parameter estimation in a stochastic intercellular network model

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