A nonlinear model to generate the winner-take-all competition

This paper is concerned with the phenomenon of winner-take-all competition. In this paper, we propose a continuous-time dynamic model, which is described by an ordinary differential equation and is able to produce the winner-take-all competition by taking advantage of selective positive–negative feedback. The global convergence is proven analytically and the convergence rate is also discussed. Simulations are conducted in the static competition and the dynamic competition scenarios. Both theoretical and numerical results validate the effectiveness of the dynamic equation in describing the nonlinear phenomena of winner-take-all competition.

[1]  T. Robbins,et al.  The neuropsychology of ventral prefrontal cortex: Decision-making and reversal learning , 2004, Brain and Cognition.

[2]  Jean-Jacques E. Slotine,et al.  Fast computation with neural oscillators , 2003, Neurocomputing.

[3]  Andrew Chi-Sing Leung,et al.  Analysis for a class of winner-take-all model , 1999, IEEE Trans. Neural Networks.

[4]  Solomon Lefschetz,et al.  Stability by Liapunov's Direct Method With Applications , 1962 .

[5]  David Dubnau.  Winner takes all in a race for cell fate , 2011, Molecular systems biology.

[6]  P. Olver.  Nonlinear Systems , 2013 .

[7]  Jean-Jacques E. Slotine,et al.  Collective Stability of Networks of Winner-Take-All Circuits , 2011, Neural Computation.

[8]  Chak-Kuen Wong,et al.  An automata network for performing combinatorial optimization , 2002, Neurocomputing.

[9]  C. Koch,et al.  Attention activates winner-take-all competition among visual filters , 1999, Nature Neuroscience.

[10]  Holger Schulze,et al.  Auditory Cortical Contrast Enhancing by Global Winner-Take-All Inhibitory Interactions , 2008, PloS one.

[11]  C. Beveridge,et al.  Update on Apical Dominance and Shoot Branching Apical Dominance and Shoot Branching. Divergent Opinions or Divergent Mechanisms? , 2006 .

[12]  Shih-Chii Liu,et al.  Computation with Spikes in a Winner-Take-All Network , 2009, Neural Computation.

[13]  Shuai Li,et al.  Winner-take-all based on discrete-time dynamic feedback , 2012, Appl. Math. Comput..

[14]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[15]  Yuguang Fang,et al.  Dynamic Analysis of a General Class of Winner-Take-All Competitive Neural Networks , 2010, IEEE Transactions on Neural Networks.

[16]  Anderson,et al.  Controlled competitive dynamics in a photorefractive ring oscillator: "Winner-takes-all" and the "voting-paradox" dynamics. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[17]  Shijun Liao,et al.  Commun Nonlinear Sci Numer Simulat , 2013 .

[18]  Marco Idiart,et al.  A Second Function of Gamma Frequency Oscillations: An E%-Max Winner-Take-All Mechanism Selects Which Cells Fire , 2009, The Journal of Neuroscience.

[19]  Cristóbal López,et al.  Species competition: coexistence, exclusion and clustering , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[20]  Shubao Liu,et al.  A Simplified Dual Neural Network for Quadratic Programming With Its KWTA Application , 2006, IEEE Transactions on Neural Networks.

[21]  Alan L. Yuille,et al.  A Winner-Take-All Mechanism Based on Presynaptic Inhibition Feedback , 1989, Neural Computation.

[22]  Simon A. J. Winder.  A model for biological winner-take-all neural competition employing inhibitory modulation of NMDA-mediated excitatory gain , 1999, Neurocomputing.