Metastability and Eye Movements: A Dynamical‑Systems Interpretation

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  1. Why metastability is a natural language for gaze behavior The idea that perception, attention, and neural activity evolve through transiently stable states has deep roots in cognitive science and neuroscience. Concepts such as attractors , basins , noise‑induced transitions , and escape times appear in work on perceptual switching, decision‑making, and neural population dynamics (Kelso, 1995; Rabinovich et al., 2008; Deco & Jirsa, 2012). Eye movements, especially the alternation between fixations and saccades ,   fit remarkably well into this metastable picture. The Freidlin–Wentzell theory of rare events (Freidlin & Wentzell, 2012) provides a rigorous mathematical language for these intuitions. 2. Fixations as metastable states  Consider the gaze position X t as the state of a stochastic dynamical system. During a fixation the  gaze remains confined to a small region, microsaccades and noise generate small fluctuations, and the gaze tends to return...
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THE TWO-ALTERNATIVE-FORCED-CHOICE (TAFC) TASK

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In most of the studies of the DM process the dynamics of the information gathering and elaboration are modeled under the so called Two-Alternative Forced-Choice (TAFC) task [1-3]. 

Choosing between two alternatives, even under time pressure and with uncertain information, is a simplification of many situations, but it is representative of many problems faced by animals in their natural environments (e.g., whether to approach or avoid a novel stimulus). The reduction of complex problems into nested easier dichotomous problems may also respond to evolutionary strategies for optimizing the speed-and-accuracy tradeoff. Bogacz and coauthors [4] evidenced that the TAFC task models typically make three fundamental assumptions:

 a) evidence favoring each alternative is integrated over time;
 b) the process is subject to random fluctuations;
 c) the decision is made when sufficient evidence has accumulated favoring one alternative   over the other. 

The major issue about the modality of integration of evidence is generally solved in favor of the integration of the difference in evidence, rather than the independent integration of evidence for each alternative. The leading theories, by assuming that the difference in evidence drives the decision, consider that  the differences can be computed by inhibitory mechanisms. Those theories essentially distinguish themselves by the mechanisms of inhibition that they adopt, by which they get to different behavioral predictions. The application of the diffusion models in the study of cognitive processes had been introduced by Ratcliff [1] and since then on they  had kept their theoretical soundness in the context of the analysis of decision making under uncertainty [2,5-12] because it is relatively simple and well characterized [13] and it has been proven to implement the optimal mechanism for TAFC decision making [14,15].



  1. Ratcliff, R. (1978). A theory of memory retrieval. Psychol Rev. 85, 59-108.
  2. Usher M., McClelland J.L. (2001). The time course of perceptual choice: the leaky, competing accumulator model. Psychol Rev. 108:550-592.
  3. Ratcliff, R., Smith, P.L. (2004). A comparison of sequential sampling models for two-choice reaction time. Psychol Rev. 111:333-367.
  4. Bogacz, R.,  Brown, E., Moehlis, J., Holmes, P., Cohen, J.D. (2006). The Physics of Optimal Decision Making: A Formal Analysis of Models of Performance in Two-Alternative Forced-Choice Tasks. Psychol Rev. 113(4): 700–765.
  5. Schall, J. D. (2001). Neural basis of deciding, choosing and acting. Nat Rev Neurosci, 2(1), 33-42.
  6. Shadlen, M. N., Newsome, W. T. (2001). Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. J Neurophysiol, 86(4), 1916-1936.
  7. Smith, P.L., Ratcliff, R. (2004). Psychlogy and biology of simple decisions. Trends Neurosci. 27(3): 161-168.
  8. Gold, J.I., Shadlen, M.N. (2002). Banburismus and the brain: decoding the relationship between sensory stimuli, decisions and reward. Neuron 36: 299-308.
  9. Hanes, D.P.,  Schall, J.D. (1996). Neural control of voluntary movement initiation. Science 274:427-430. 
  10. Ratcliff, R. (1998). The role of mathematical psychology in experimental psychology. Aust J Psychol. 50: 129-130.
  11. Ratcliff, R., Tuerlinckx, F. (2002). Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability. Psychon Bull Rev. 9: 438-481.
  12. Ratcliff, R., Cherian, A., Segraves, M. (2003). A comparison of macaque behavior and superior colliculus neuronal activity to predictions from models of simple two-choice decisions. Journal Neurophysiol. 90:1392-1407.
  13. Smith P.L. (2000). Stochastic dynamic models of response time and accuracy: a fundational primer. J Math Psychol. 44: 408-463.
  14. Bogacz, R., Gurney, K. (2007). The basal ganglia and cortex implement optimal decision making between alternative actions. Neural Comput 19(2):442-477.
  15. Laming, D. R. J. (1968). Information theory of choice-reaction times. Wiley, NewYork.

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