Instabilities and Phase Transitions in Human Brain and Behavior

One hazard of interdisciplinary research is that important results in one fi eld may be unknown or totally ignored in another. To ensure that this does not happen, editors and reviewers have an even more diffi cult job and greater responsibility than usual. Scheffer et al.’s (2009) recent review is a case in point. The authors identify ‘early warning signals’ such as critical slowing down in simple nonlinear models and suggest these may now be helpful in predicting upcoming transitions (‘tipping points’ in the modern idiom) in ‘real systems’ such as the climate, ecosystems and fi nancial markets. Here I describe briefl y work that used an intimate blend of theoretical concepts from the fi eld of nonequilibrium physics (Haken, 1977/83; Sornette, 2000), mathematical modeling and experiments on humans to establish early warning signals and their signifi cance for biological coordination. Though the research was published in prominent journals it may be worth considering the reasons why Scheffer et al. and their reviewers missed it. Scheffer et al.’s strategy is to present simple catastrophe theoretic models and suggest that some of the features they contain prior to bifurcation such as critical slowing down and increased variance may also be found in very different complex systems. Their case would have been stronger had they demonstrated an explicit connection between the phenomena observed and the theoretical concepts and mathematical models used to explain them. Failing that, the authors might have referred to other ‘real systems’ where this has been done. Take the voluntary movements of the two hands, a system that has proved a window into tipping points and self-organization in complex biological systems. Very many sensory and motor elements are involved, neurons, muscles, joints, metabolic processes, etc. Yet when human subjects are asked to rhythmically move their index fi ngers they do so in one of only two patterns: an alternating, out of phase pattern where the fi ngers move in the same direction and a symmetric in-phase pattern where homologous muscles contract simultaneously. Under instructions to start moving in the anti-phase pattern and increase rate of movement, a spontaneous transition to in-phase occurs at a critical rate. Slowing down after the switch does not return the system to the initial pattern. No transitions occur when subjects start inphase (Kelso, 1984). The simplest dynamics that captures all the observed empirical facts is: