Gonzalo G. Izús

Critical slowing-down in the FitzHugh–Nagumo model: A non-equilibrium potential approach

Abstract We exploit our recent finding of an exact non-equilibrium potential (NEP) for the space-independent FitzHugh–Nagumo (FHN) model [Phys. Rev. E 58 (1998) 93], to characterize the transition from the bistable regime towards the excitable one. The critical slowing-down (CSD) is clearly seen in the time-evolution of the NEP.

Highly synchronized noise‐driven oscillatory behavior of a FitzHugh—Nagumo ring with phase‐repulsive coupling

We investigate a ring of N FitzHugh‐Nagumo elements coupled in phase‐repulsive fashion and submitted to a (subthreshold) common oscillatory signal and independent Gaussian white noises. This system can be regarded as a reduced version of the one studied in [Phys. Rev. E 64, 041912 (2001)], although externally forced and submitted to noise. The noise‐sustained synchronization of the system with the external signal is characterized.

Global analysis of pattern selection and bifurcations in monostable reaction-diffusion systems

We study a piecewise linear version of a one-component monostable reaction diffusion model in a bounded domain, subjected to partially reflecting boundary conditions (“albedo” b.c.). We analyze the local and the global stability of the merging patterns and detect a bifurcation of the uniform solution induced by changes in the reflectivity of the boundaries.

CONTROL OF REACTANT FLOW AT THE BOUNDARY : ITS EFFECT ON THE ONSET OF NONEQUILIBRIUM MACROSCOPIC STRUCTURES IN CHEMICAL REACTIONS

In a one‐dimensional, two‐component excitable chemical model system (the ‘‘Brusselator’’) we investigate the effects of controlling the flow of reactants at the boundary, on the stability of the thermodynamical branch. The reflectivity of the boundary adjusts the external flux and acts as a control parameter, capable of enhancing or weakening the self‐organizing processes leading to the appearance of temporal or spatial patterns.

Complete synchronization of convective patterns between Gray–Scott systems

Abstract.Two identical 1D autocatalytic systems with Gray–Scott kinetics—driven towards convectively unstable regimes and submitted to independent spatiotemporal Gaussian white noises—are coupled unidirectionally, but otherwise linearly. Numerical simulation then reveals that (even when perturbed by noise) the slave system replicates the convective patterns arising in the master one to a very high degree of precision, as indicated by several measures of synchronization.

Diffusive feed of reactants and Hopf bifurcations in an oscillatory reaction-diffusion model

We study an oscillatory chemical model (the “Brusselator”) with the aim of analyzing the effect of a controlled diffusive feed of reactants in the appearance of chemical oscillations. The reflectivities of the boundary, which adjust the external fluxes, act as control parameters capable to alter the attractive basin of the thermodynamic branch, leading to oscillatory behavior.