Dynamical system theory has been applied in the field of neuroscience and cognitive development, especially in the neo-Piagetian theories of cognitive development. It is the belief that cognitive development is best represented by physical theories rather than theories based on syntax and AI. It also believed that differential equations are the most appropriate tool for modeling human behavior. These equations are interpreted to represent an agent's cognitive trajectory through state space. In other words, dynamicists argue that psychology should be (or is) the description (via differential equations) of the cognitions and behaviors of an agent under certain environmental and internal pressures. The language of chaos theory is also frequently adopted. In it, the learner's mind reaches a state of disequilibrium where old patterns have broken down. This is the phase transition of cognitive development. Self-organization (the spontaneous creation of coherent forms) sets in as activity levels link to each other. Newly formed macroscopic and microscopic structures support each other, speeding up the process. These links form the structure of a new state of order in the mind through a process called scalloping (the repeated building up and collapsing of complex performance.) This new, novel state is progressive, discrete, idiosyncratic and unpredictable.[4] Dynamic systems theory has recently been used to explain a long-unanswered problem in child development referred to as the A-not-B error.[5] Jean Piaget's theory of cognitive development has been criticized on many grounds. One criticism is concerned with the very nature of development itself. It is suggested that Piaget's theory does not explain why development from stage to stage occurs. The theory is also criticized for ignoring individual differences in cognitive development. That is, the theory does not account for the fact that some individuals move from stage to stage faster than other individuals. Finally, another criticism is concerned with the nature of stages themselves. Research shows that the functioning of a person at a given age may be so variable from domain to

omain, such as the understanding of social, mathematical, and spatial concepts, that it is not possible to place the person in a single stage.[1] To remove these weaknesses, a group of researchers, who are known as neo-Piagetian theorists, advanced models that integrate concepts from Piaget's theory with concepts from cognitive and differential psychology.Neural oscillation is rhythmic or repetitive neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms localized within individual neurons or by interactions between neurons. In individual neurons, oscillations can appear either as oscillations in membrane potential or as rhythmic patterns of action potentials, which then produce oscillatory activation of post-synaptic neurons. At the level of neural ensembles, synchronized activity of large numbers of neurons can give rise to macroscopic oscillations, which can be observed in the electroencephalogram (EEG). Oscillatory activity in groups of neurons generally arises from feedback connections between the neurons that result in the synchronization of their firing patterns. The interaction between neurons can give rise to oscillations at a different frequency than the firing frequency of individual neurons. A well-known example of macroscopic neural oscillations is alpha activity. Neural oscillations were observed by researchers as early as Hans Berger, but their functional role is still not fully understood. The possible roles of neural oscillations include feature binding, information transfer mechanisms and the generation of rhythmic motor output. Over the last decades more insight has been gained, especially with advances in brain imaging. A major area of research in neuroscience involves determining how oscillations are generated and what their roles are. Oscillatory activity in the brain is widely observed at different levels of observation and is thought to play a key role in processing neural information. Numerous experimental studies indeed support a functional role of neural oscillations; a unified interpretation, however, is still lacking.

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