Phase Transitions, Neural Population Models and
A neural population model pictures the cortex as a continuum of excitable tissue comprised of densely interconnected excitatory and inhibitory neurons, with cortical activity encoded as population-average firing rates. For certain ranges of cortical parameters, such models can exhibit multistability, with access to multiple equilibrium (homogeneous and stationary) and nonequilibrium (patterned or dynamic) spatiotemporal states. These distinct states may be identified with particular phases of normal and pathological brain activity such as wakefulness, anesthetic coma, and seizure. Transitions between states can be induced by variations in a control parameter such as neurotransmitter concentration and subcortical stimulation and can be likened to the thermodynamic phase transitions (e.g., melting, freezing) of physical science.
Equilibrium Phase Transitions
KeywordsHopf Bifurcation Nonequilibrium Phase Transition Equilibrium Phase Transition Turing Bifurcation Thermodynamic Phase Transition
- Liley DTJ, Bojak I (2005) Understanding the transition to seizure by modeling the epileptiform activity of general anesthetic agents. Clin Neurophysiol 22(5):300–313Google Scholar
- Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. Wiley, New YorkGoogle Scholar
- Steyn-Ross ML, Steyn-Ross DA, Sleigh JW (2013) Interacting turing-hopf instabilities drive symmetry-breaking transitions in a mean-field model of the cortex: a mechanism for the slow oscillation. Phys Rev X 3(2):021,005. doi: 10.1103/PhysRevX.3.021005, url: http://link.aps.org/doi/10.1103/PhysRevX.3.021005