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Determinism is a special property of some systems and is defined by its state-space behavior in which the trajectories in time never intersect. Whether or not determinism exists in brain activities is a question that may be resolved by analysis of the dynamical properties of the electroencephalogram (EEG) or magnetoencephalogram (MEG). We will show that even though there are strong nonstationarities in most brain behaviors, small epochs of deterministic dynamics can still be observed. We will also show that the local Lyapunov exponents are measures that can demonstrate smooth transitions into these deterministic states.
The long-term objective is to understand how large masses of neurons in the brain process information during various learning and memory paradigms. Both time- and space-dependent processes have been identified in animals through computer-based analytic quantifications of event-related extracellular potentials. New nonlinear analyses have been introduced that presume that the fine-grain variation in the signal is determined and patterned in phase-space. Some neurons in the primary visual cortex manifest gamma-band oscillations. These cells show both a nonspecific phase-alignment (response synchrony) and a specific tuning (orientation tuning) when stimuli are presented to their receptive fields. This dual regulation of the sensory cells is proposed to underlie stimulus binding, a theoretical mechanism for "object" perception. Nonlinear analytic results from gamma-activities in a simple model neuropil (olfactory bulb) suggest that neuroplasticity may arise through self-organization, a process in which a nonlinear change in the dynamics of the oscillatory field potentials is the hallmark. This self-organization may follow simple dynamical laws in which global cooperativity among the neurons is transiently brought about that, over trials, results in enduring changes in the nonlinear dynamics of some neurons. In conclusion, the sculpturing of the synaptic throughput in the sensory cortex (stimulus binding) may be associated with the irregular phases of the gamma-activities and may result from both specific and nonspecific systems operating together in a nonlinear self-organizing manner.
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