arXiv subjects
Publications and source records attributed to F. J. de la Rubia.
We study the response of an attractor neural network, in the ferromagnetic phase, to an external, time-dependent stimulus, which drives the system periodically two different attractors. We demonstrate a non-trivial dependance of the system via a system size resonance, by showing a signal amplification maximum at a certain finite size.
We study the spread of Hantavirus over a host population of deer mice using a population dynamics model. We show that taking into account the internal fluctuations in the mouse population due to its discrete character strongly alters the behaviour of the system. In addition to the familiar transition present in the deterministic model, the inclusion of internal fluctuations leads to the emergence of an additional deterministically hidden transition. We determine parameter values that lead to maximal propagation of the disease, and discuss some implications for disease prevention policies.
We study a generic reaction-diffusion model for single-species population dynamics that includes reproduction, death, and competition. The population is assumed to be confined in a refuge beyond which conditions are so harsh that they lead to certain extinction. Standard continuum mean field models in one dimension yield a critical refuge length L_c such that a population in a refuge larger than this is assured survival. Herein we extend the model to take into account the discreteness and finiteness of the population, which leads us to a stochastic description. We present a particular critical criterion for likely extinction, namely, that the standard deviation of the population be equal to the mean. According to this criterion, we find that while survival can no longer be guaranteed for any refuge size, for sufficiently weak competition one can make the refuge large enough (certainly larger than L_c) to cause extinction to be unlikely. However, beyond a certain value of the competition rate parameter it is no longer possible to escape a likelihood of extinction even in an infinite refuge. These unavoidable fluctuations therefore have a severe impact on refuge design issues.
Using a model for rodent population dynamics, we study outbreaks of Hantavirus infection induced by the alternation of seasons. Neither season by itself satisfies the environmental requirements for propagation of the disease. This result can be explained in terms of the seasonal interruption of the relaxation process of the mouse population toward equilibrium, and may shed light on the reported connection between climate variations and outbreaks of the dise ase.
We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic resonancelike behavior with the noise correlation time, there is an effect of optimal localization of the system trajectories in the phase space. This phenomenon is observed in systems with different nonlinearities, suggesting a degree of universality.