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This article presents an idealized mathematical model of the cerebral cortex, focusing on the dynamical interaction of neurons. The author proposes a network architecture more consistent with neuroanatomy than in previous studies, borrows ideas from nonequilibrium statistical mechanics and calls attention to the fact that the brain is a large and complex dynamical system. The ideas proposed are illustrated with a realistic model of the visual cortex. [ABSTRACT FROM AUTHOR]

We propose a model of Sinai billiards with moving scatterers, in which the locations and shapes of the scatterers may change by small amounts between collisions. Our main result is the exponential loss of memory of initial data at uniform rates, and our proof consists of a coupling argument for non-stationary compositions of maps similar to classical billiard maps. This can be seen as a prototypical result on the statistical properties of time-dependent dynamical systems. [ABSTRACT FROM AUTHOR]

The article explores the evolution of a chaotic dynamic system. It examines the three standard ways in which dynamical complexity or chaos manifests itself which include hyperbolicity, entropy and correlation decay. It discusses the problem of proving the existence or nonexistence of chaotic behavior in systems defined by concrete equations. It also illustrates a class of strange attractors that arise naturally in simplified models of physics and biology.