title: Microscopic instability in recurrent neural networks.
abstract: In a manner similar to the molecular chaos that underlies the stable thermodynamics of gases, a neuronal system may exhibit microscopic instability in individual neuronal dynamics while a macroscopic order of the entire population possibly remains stable. In this study, we analyze the microscopic stability of a network of neurons whose macroscopic activity obeys stable dynamics, expressing either monostable, bistable, or periodic state. We reveal that the network exhibits a variety of dynamical states for microscopic instability residing in a given stable macroscopic dynamics. The presence of a variety of dynamical states in such a simple random network implies more abundant microscopic fluctuations in real neural networks which consist of more complex and hierarchically structured interactions.
authors: Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
authors: Yuzuru
authors: Y
authors: Yamanaka
authors: RIKEN Brain Science Institute, Hirosawa 2-1, Wako-shi, Saitama 351-0198, Japan.
authors: Shun-ichi
authors: S
authors: Amari
authors: Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
authors: Shigeru
authors: S
authors: Shinomoto
mesh_terms: D008959:Models, Neurological; D009415:Nerve Net / Q000166:cytology*; D009474:Neurons; D017711:Nonlinear Dynamics