Deterministic analysis of stochastic bifurcations in multi-stable neurodynamical systems

Many perceptual and cognitive processes, like decision-making and bistable perception, involve multistable phenomena under the influence of noise. The role of noise in a multistable neurodynamical system can be formally treated within the Fokker–Planck framework. Nevertheless, because of the underlying nonlinearities, one usually considers numerical simulations of the stochastic differential equations describing the original system, which are time consuming. An alternative analytical approach involves the derivation of reduced deterministic differential equations for the moments of the distribution of the activity of the neuronal populations. The study of the reduced deterministic system avoids time consuming computations associated with the need to average over many trials. We apply this technique to describe multistable phenomena. We show that increasing the noise amplitude results in a shifting of the bifurcation structure of the system.

[1]  Ranulfo Romo,et al.  Flexible Control of Mutual Inhibition: A Neural Model of Two-Interval Discrimination , 2005, Science.

[2]  R. Romo,et al.  Neuronal Correlates of a Perceptual Decision in Ventral Premotor Cortex , 2004, Neuron.

[3]  Emilio Salinas,et al.  Cognitive neuroscience: Flutter Discrimination: neural codes, perception, memory and decision making , 2003, Nature Reviews Neuroscience.

[4]  P. Glimcher.  Indeterminacy in brain and behavior. , 2005, Annual review of psychology.

[5]  H. Tuckwell,et al.  Statistical properties of stochastic nonlinear dynamical models of single spiking neurons and neural networks. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  E. Rolls,et al.  Decision‐making and Weber's law: a neurophysiological model , 2006, The European journal of neuroscience.

[7]  Carson C. Chow,et al.  A Spiking Neuron Model for Binocular Rivalry , 2004, Journal of Computational Neuroscience.

[8]  Ranulfo Romo,et al.  Basic mechanisms for graded persistent activity: discrete attractors, continuous attractors, and dynamic representations , 2003, Current Opinion in Neurobiology.

[9]  N. P. Bichot,et al.  Perceptual and motor processing stages identified in the activity of macaque frontal eye field neurons during visual search. , 1996, Journal of neurophysiology.

[10]  P. Glimcher.  decisions, uncertainty and the brain , 2003 .

[11]  Metastable states in a nonlinear stochastic model , 1984 .

[12]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[13]  Jeffrey D. Schall,et al.  Neural basis of deciding, choosing and acting , 2001, Nature Reviews Neuroscience.

[14]  J. Gold,et al.  Representation of a perceptual decision in developing oculomotor commands , 2000, Nature.

[15]  D. Amit,et al.  Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. , 1997, Cerebral cortex.

[16]  M. Mattia,et al.  Population dynamics of interacting spiking neurons. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  N. Logothetis,et al.  Multistable phenomena: changing views in perception , 1999, Trends in Cognitive Sciences.

[18]  M N Shadlen,et al.  Motion perception: seeing and deciding. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[19]  R. Ratcliff,et al.  Connectionist and diffusion models of reaction time. , 1999, Psychological review.

[20]  M. M. Taylor,et al.  Stochastic processes in reversing figure perception , 1974 .

[21]  Maurizio Mattia,et al.  Finite-size dynamics of inhibitory and excitatory interacting spiking neurons. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Philip L. Smith,et al.  Psychology and neurobiology of simple decisions , 2004, Trends in Neurosciences.

[23]  Hugh R Wilson,et al.  Computational evidence for a rivalry hierarchy in vision , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Colin Renfrew,et al.  Carbon 14 and the Prehistory of Europe , 1971 .

[25]  F. Attneave.  Multistability in perception. , 1971, Scientific American.

[26]  Gustavo Deco,et al.  Computational neuroscience of vision , 2002 .

[27]  Walter Senn,et al.  Minimal Models of Adapted Neuronal Response to In VivoLike Input Currents , 2004, Neural Computation.

[28]  J. Gold,et al.  Banburismus and the Brain Decoding the Relationship between Sensory Stimuli, Decisions, and Reward , 2002, Neuron.

[29]  Jianfeng Feng,et al.  Computational neuroscience , 1986, Behavioral and Brain Sciences.

[30]  Xiao-Jing Wang,et al.  Mean-Field Theory of Irregularly Spiking Neuronal Populations and Working Memory in Recurrent Cortical Networks , 2003 .

[31]  R. Romo,et al.  Touch and go: decision-making mechanisms in somatosensation. , 2001, Annual review of neuroscience.

[32]  H C Tuckwell,et al.  Noisy spiking neurons and networks: useful approximations for firing probabilities and global behavior. , 1998, Bio Systems.

[33]  Michael L. Platt,et al.  Neural correlates of decision variables in parietal cortex , 1999, Nature.

[34]  James L. McClelland,et al.  The time course of perceptual choice: the leaky, competing accumulator model. , 2001, Psychological review.

[35]  Henry C. Tuckwell,et al.  Analytical and Simulation Results for Stochastic Fitzhugh-Nagumo Neurons and Neural Networks , 1998, Journal of Computational Neuroscience.