Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: ͑i͒ Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. ͑ii͒ In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. ͑iii͒ Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. ͑iv͒ The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. ͑v͒ Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?

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We report experimental studies of synchronization phenomena in a pair of biological neurons that interact through naturally occurring, electrical coupling. When these neurons generate irregular bursts of spikes, the natural coupling synchronizes slow oscillations of membrane potential, but not the fast spikes. By adding artificial electrical coupling we studied transitions between synchrony and asynchrony in both slow oscillations and fast spikes. We discuss the dynamics of bursting and synchronization in living neurons with distributed functional morphology.Comment: 4 pages, 6 figures, to be published in PR

There are now a reasonable number of invertebrate central pattern generator (CPG) circuits described in sufficient detail that a mechanistic explanation of how they work is possible. These small circuits represent the best-understood neural circuits with which to investigate how cell-tocell synaptic connections and individual channel conductances combine to generate rhythmic and patterned output. In this review, some of the main lessons that have appeared from this analysis are discussed and concrete examples of circuits ranging from single phase to multiple phase patterns are described. While it is clear that the cellular components of any CPG are basically the same, the topology of the circuits have evolved independently to meet the particular motor requirements of each individual organism and only a few general principles of circuit operation have emerged. The principal usefulness of small systems in relation to the brain is to demonstrate in detail how cellular infrastructure can be used to generate rhythmicity and form specialized patterns in a way that may suggest how similar processes might occur in more complex systems. But some of the problems and challenges associated with applying data from invertebrate preparations to the brain are also discussed. Finally, I discuss why it is useful to have well-defined circuits with which to examine various computational models that can be validated experimentally and possibly applied to brain circuits when the details of such circuits become available.

A simple technique for rapidly killing all or part of single neurons consists of filling the cell with Lucifer Yellow CH and irradiating all or part of it with intense blue light. Such treatment kills the irradiated part of the cell within a few minutes. Adjacent cells are not affected.