Correlation between eigenvalue spectra and dynamics of neural networks.
This letter presents a study of the correlation between the eigenvalue spectra of synaptic matrices and the dynamical properties of asymmetric neural networks with associative memories. For this type of neural network, it was found that there are essentially two different dynamical phases: the chaos phase, with almost all trajectories converging to a single chaotic attractor, and the memory phase, with almost all trajectories being attracted toward fixed-point attractors acting as memories. We found that if a neural network is designed in the chaos phase, the eigenvalue spectrum of its synaptic matrix behaves like that of a random matrix (i.e., all eigenvalues lie uniformly distributed within a circle in the complex plan), and if it is designed in the memory phase, the eigenvalue spectrum will split into two parts: one part corresponds to a random background, the other part equal in number to the memory attractors. The mechanism for these phenomena is discussed in this letter.
Zhou
Qingguo
Q
School of Information Science and Engineer, Lanzhou University, and Engineering Research Center of Open Source Software and Realtime Operating System, Ministry of Education, Lanzhou 730000, PRC. zhouqg@lzu.edu.cn
Jin
Tao
T
Zhao
Hong
H
D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D001921:Brain / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D008568:Memory / Q000502:physiology*; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D009435:Synaptic Transmission / Q000502:physiology