Coexistence of exponentially many chaotic spin-glass attractors.
A chaotic network of size N with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load α = P/N < 1, where P stands for the number of stored patterns, the chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with α. At finite α, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with N. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the N chaotic units or freezing with respect to the P patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.
Department of Physics, Bar-Ilan University, IL-52900 Ramat-Gan, Israel.
Y
Y
Peleg
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M
Zigzag
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W
Kinzel
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I
Kanter