Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.

Concentration inequalities and laws of large numbers under epistemic and regular irrelevance

This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance that are expressed using lower and upper expectations. The results build upon De Cooman and Miranda`s recent inequalities and laws of large numbers. The proofs indicate connections between the theory of martingales and concepts of epistemic and regular irrelevance. (C) 2010 Elsevier Inc. All rights reserved.

Sexual differentiation of cortical spreading depression propagation after acute and kindled audiogenic seizures in the Wistar audiogenic rat (WAR)

Brain excitability diseases like epilepsy constitute one factor that influences brain electrophysiological features. Cortical spreading depression (CSD) is a phenomenon that can be altered by changes in brain excitability. CSD propagation was presently characterized in adult mate and female rats from a normal Wistar strain and from a genetically audiogenic seizure-prone strain, the Wistar audiogenic rat (WAR), both previously submitted (RAS(+)), or not (RAS(-)), to repetitive acoustic stimulation, to provoke audiogenic kindling in the WAR-strain. A gender-specific change in CSD-propagation was found. Compared to seizure-resistant animals, in the RAS- condition, mate and female WARs, respectively, presented CSD-propagation impairment and facilitation, characterized, respectively, by lower and higher propagation velocities (P<0.05). In contraposition, in the RAS(+) condition, mate and female WARs displayed, respectively, higher and tower CSD-propagation rates, as compared to the corresponding controls. In some Wistar and WAR females, we determined estrous cycle status on the day of the CSD-recording as being either estrous or diestrous; no cycle-phase-related differences in CSD-propagation velocities were detected. In contrast to other epilepsy models, such as Status Epilepticus induced by pilocarpine, despite the CSD-velocity reduction, in no case was CSD propagation blocked in WARs. The results suggest a gender-related, estrous cycle-phase-independent modification in the CSD-susceptibility of WAR rats, both in the RAS(+) and RAS(-) situation. (C) 2008 Elsevier B.V. All rights reserved.