The Brain at the Edge of Chaos

Although the brain is frequently compared against a computer, at present we are not clear how brain functions may be recasted in computational terms. Specifically, we lack understanding of how the brain represents or transforms information, nor do we recognize the logical operations used. In the late 1990s, Kauffman, Langton, and Packard suggested that life exists at the Edge of Chaos. Through the works of Bak, Beggs, and Bullmore, scientists have come to suspect that the brain might also be a self-organized structure that functions at the edge of chaos. We aim to investigate the implications of this idea, by considering brain models consisting of complex networks of nonlinear neuronal equations. In our preliminary studies of the Izhikevich neuron model, we discovered a parameter region with high density of qualitatively distinct states. Such a parameter region can be identified as the Edge of Chaos. We then coupled the neuron equations parametrically, so that each neuron transits between parameter regions as a result of the dynamics of involving its neighbors. We aim to demonstrate that information can be encoded and transform in this manner. In addition, we hope to use this as a basis for understanding the development of the human brain from infant to adult. Ultimately, a theory of how the brain computes will allow us to (1) seek novel cures and remedies to neurological disorders like epilepsy, dementia, autism, and attention deficiency disorder; (2) provide neuroscience basis to education and pedagogy, to open the doors for science-based curriculum planning; and (3) design brain-mimetic supercomputers that are radically different from modern digital computers.