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Bifurcation analysis in an associative memory model.

Masaki Kawamura1, Ryuji Tokunaga, Masato Okada

  • 1Faculty of Science, Yamaguchi University, Yoshida 1677-1, Yamaguchi, 753-8512, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
PubMed
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Adding temperature to a nonmonotonic sequential associative memory model eliminates chaos. This finite-temperature model exhibits coexisting attractors, unlike the absolute zero model, revealing temperature

Area of Science:

  • Computational neuroscience
  • Statistical mechanics
  • Dynamical systems theory

Background:

  • Previous research demonstrated chaos in a nonmonotonic sequential associative memory model at absolute zero.
  • The frustration of interaction in this model was identified as the source of chaotic behavior.

Purpose of the Study:

  • To analyze bifurcation phenomena in a stochastic, finite-temperature version of the nonmonotonic sequential associative memory model.
  • To investigate the impact of temperature on the model's dynamics, specifically the emergence of attractors and the disappearance of chaos.

Main Methods:

  • Derivation of order-parameter equations from stochastic microscopic equations.
  • Analysis of two-parameter bifurcation diagrams generated from these derived equations.

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Main Results:

  • The finite-temperature model exhibits the coexistence of attractors, a phenomenon not observed at absolute zero.
  • Temperature effects lead to the disappearance of chaotic behaviors previously reported at absolute zero.

Conclusions:

  • Temperature plays a crucial role in stabilizing the dynamics of the nonmonotonic sequential associative memory model.
  • The introduction of thermal fluctuations alters the phase space, leading to new emergent behaviors like coexisting attractors and suppressing chaos.