Complex dynamics for a reduced model of human EEG: implications for the physiological basis of brain activity
© Buente et al; licensee BioMed Central Ltd. 2011
Published: 18 July 2011
A number of highly nontrivial mechanisms for the birth of complexity are present in these reduced equations, among which we particularly note: i) chaos, generated by a Shilnikov saddle-node bifurcation, that acts as an organizing centre for the parameter space, ii) appearance of stable and unstable resonant bifurcation points responsible for quasiperiodic oscillations within EEG bands (e.g., alpha-gamma resonances), iii) existence of a number of oscillatory phenomena with biological relevance, such as mixed mode oscillations and multistability and iv) bursts and seizure-like dynamics for extended ranges of parameters. Based on this reduced model there are some speculative questions that we would like to propose in this poster. Firstly, is it possible to define a maximal number of degrees of freedom in neural field models that are sufficient to capture the relevant activity of mammalian cortex at rest? The high dimensionality and large parameter spaces of many of the existing models and theories of cortical dynamics discourages an in-depth, rigorous mathematical analysis, which are typically performed for models of spike generation. Secondly, can we be guided by reduced models in establishing a “hierarchy” of physiological causes for observed electrical brain patterns? And, finally, how do some of the findings presented here enrich our knowledge of the biological basis for rhythmic brain activity? For instance, our analysis points to resonances in human EEG being triggered by a physiological cause rather than being the product of complex synchronization mechanisms .
- Liley DTJ, Cadusch PJ, Dafilis MP: A spatially continuous mean field theory of electrocortical activity. Network: Comput. Neural Syst. 2002, 13: 67-113.View ArticleGoogle Scholar
- Frascoli F, Van Veen L, Bojak I, Liley DTJ: Metabifurcation analysis of a mean field model of the cortex. accepted in Physica D, arXiv:1008.4043Google Scholar
- Palva JM, Palva S, Kaila K: Phase Synchrony among Neuronal Oscillations in the Human Cortex. J. Neuroscience. 2005, 25: 3962-3972. 10.1523/JNEUROSCI.4250-04.2005.View ArticlePubMedGoogle Scholar
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