Office: 116 Krasnow Institute Phone: 703.993.4431
Personal Website: http://complex.gmu.edu/people/ernie/
Other Websites: http://barreto.spacs.gmu.edu/
Current Research Interests
The main goal of my research is to understand and describe the complex dynamics in neural systems using techniques from dynamical systems theory. We are specifically interested in the emergence of collective behavior across the various scales of neuronal organization, from individual neurons to various functional ensembles.
In the past decade, our laboratory has been successful in establishing that dynamics from single neurons,small ensembles of neurons, and from intact human cortical recordings show significant degrees of nonlinear determinism. This result was derived using concepts from nonlinear dynamics theory; specifically that a system with relatively few degrees of freedom can exhibit highly complex behavior, and that such dynamics can be decomposed into a hierarchy of unstable periodic orbits (UPOs). These orbits are the equilibrium states of the system, but, since they are unstable, the actual dynamics tend to be a series of close approaches and subsequent divergences from them. We have developed a highly effective method for extracting hierarchies of UPOs from experimental data, along with approximations of the dynamics near them
Biological Physics Classical Mechanics