Patterns of phase-dependent spiral wave attenuation in excitable media.

We show that introducing periodic planar fronts with long excitation duration can lead to spiral attenuation. The attenuation occurs periodically over cycles of several planar fronts, forming a variety of complex spatiotemporal patterns. We find that these attenuation patterns occur only at specific phases of the descending fronts relative to the rotational phase of the spiral. These patterns fall into two general classes, each defined by a specific expression for the number of attenuated spirals per cycle of planar fronts, and represented by a structured diagram in parameter space. The spiral attenuation patterns we observe remain stable in time and do not change during the evolution of the system.

System-size resonance in a binary attractor neural network.

System size resonance (SSR) is a phenomenon in which the response of a system is optimal for a certain finite size, but poorer as the size goes to zero or infinity. In order to show SSR effects in binary attractor neural networks, we study the response of a network, in the ferromagnetic phase, to an external, time-dependent stimulus. Under the presence of such a stimulus, the network shows SSR, as is demonstrated by the measure of the signal amplification both analytically and by simulation.

Outbreaks of Hantavirus induced by seasonality.

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 disease.

Extinction in population dynamics.

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.

Effects of internal fluctuations on the spreading of Hantavirus.

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 behavior 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.

Coherence enhancement in nonlinear systems subject to multiplicative Ornstein-Uhlenbeck noise.

We show that for two biologically relevant models with self-sustained oscillations under the action of a multiplicative Ornstein-Uhlenbeck process, their coherence response behaves nonmonotonically with the process correlation time. There is a correlation time for which the quality factor is optimized. This phenomenon is a consequence of the interplay between the correlation time and the system's periodicity. This relation is evidenced through a power law relation with an exponent close to -1 / 2.

Random Ginzburg-Landau model revisited: reentrant phase transitions.

We analyze the phase diagram of the random Ginzburg-Landau model, where a quenched dichotomous noise affects the control parameter. We show that the system exhibits two types of counterintuitive reentrant second-order phase transitions. In the first case, increasing the coupling drives the system from a disordered to an ordered state and then back to a disordered state. In the second case, increasing the intensity of the quenched noise, the system goes from an ordered phase to a disordered phase and back to an ordered state. We discuss the general mechanism that produces these reentrant phase transitions, showing that it may appear in other physical systems, such as a modification of the spin-1 Blume-Capel model proposed to describe the critical behavior of helium mixtures in a random medium.