Alpha rhythm and hypofrontality in schizophrenia.

OBJECTIVE: To reveal the EEG correlates of resting hypofrontality in schizophrenia (SZ). METHOD: We analyzed the whole-head EEG topography in 14 patients compared to 14 matched controls by applying a new parameterization of the multichannel EEG. We used a combination of power measures tuned for regional surface mapping with power measures that allow evaluation of global effects. RESULTS: The SZ-related EEG abnormalities include i) a global decrease in absolute EEG power robustly manifested in the alpha and beta frequency bands, and ii) a relative increase in the alpha power over the prefrontal brain regions against its reduction over the posterior regions. In the alpha band both effects are linked to the SZ symptoms measured with Positive and Negative Symptom Scales and to chronicity. CONCLUSION: As alpha activity is related to regional deactivation, our findings support the concept of hypofrontality in SZ and expose the alpha rhythm as a sensitive indicator of it.

Singular homoclinic bifurcations in tritrophic food chains.

The Rosenzweig-MacArthur food chain model is proved to have homoclinic orbits. The proof is in two steps. First, we use a geometric approach based on singular perturbation and detect singular homoclinic orbits as well as parameter combinations for which these orbits exist. Second, we show, numerically, that for slightly different parameter values there exist also nonsingular homoclinic orbits that tend toward the singular ones when the time responses of the three trophic levels are extremely diversified. The analysis is performed without exploiting too deeply the mathematical structure of the Rosenzweig-MacArthur model. This is done intentionally, to assist readers interested more in the methodology than in the application to food chains.

Yield and dynamics of tritrophic food chains.

Strong relationships between yield and dynamic behavior of tritrophic food chains are pointed out by analyzing the classical Rosenzweig-MacArthur model. On the one hand, food chains are subdivided into undersupplied and oversupplied categories, the first being those in which a marginal increase of nutrient supply to the bottom produces a marginal increase of mean yield at the top. On the other hand, a detailed bifurcation analysis proves that dynamic complexity first increases with nutrient supply (from stationary to a low-frequency cyclic regime and, finally, to chaos) and then decreases (from chaos to a high-frequency cyclic regime). A careful comparison of the two analyses supports the conclusion that food chains cycling at high frequency are oversupplied, while all others are undersupplied. A straightforward consequence of this result is that maximization of food yield requires a chaotic regime. This regime turns out to be very often on the edge of a potential catastrophic collapse of the top component of the food chain. In other words, optimality implies very complex and dangerous dynamics, as intuitively understood long ago for ditrophic food chains by Rosenzweig in his famous article on the paradox of enrichment.