Dynamics of Activity in Biology-Oriented Neural Network Models: Stability at Low Firing Rates

We investigated the dynamics of activity in feedback neural network models at low firing rates. The networks were designed to capture the typical features of real cortical networks. Stability analysis of the linearized model and simulations of different degrees of complexity show that stability is only obtained for very fast and sufficiently strong inhibition; otherwise the network activity develops into synchronous oscillations with frequency and amplitude dynamics governed predominantly by the inhibition parameters, but largely independent of (1) the network architecture (uniform, random or structured), (2) the spiking or analog nature of the neural activity, and, albeit to a lesser extent, (3) the linear or nonlinear nature of the neural threshold function. Provided the network connectivity is sufficiently rich and structured, the spike activity exhibits features which resemble those observed in physiological recordings from various cortical areas: cell assembly behaviour with different, simultaneous correlation dynamics (event coherence and rate coherence).

[1]  E. Ahissar,et al.  Correlated Activity of Neurons: A Neural Code for Higher Brain Functions? , 1991 .

[2]  Michael Erb.  Simulation neuronaler Netze: Stabilität, Plastizität und Konnektivität , 1992 .

[3]  A Treves,et al.  Associative memory neural network with low temporal spiking rates. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[4]  C. von der Malsburg,et al.  Am I Thinking Assemblies , 1986 .

[5]  M. Soha,et al.  A distributed approach to lan monitoring using intelligent high performance monitors , 1987, IEEE Network.

[6]  F. Attneave,et al.  The Organization of Behavior: A Neuropsychological Theory , 1949 .

[7]  Professor Moshe Abeles,et al.  Local Cortical Circuits , 1982, Studies of Brain Function.

[8]  Moshe Abeles,et al.  Corticonics: Neural Circuits of Cerebral Cortex , 1991 .

[9]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[10]  Christoph von der Malsburg,et al.  The Correlation Theory of Brain Function , 1994 .

[11]  T. M. Mayhew,et al.  Anatomy of the Cortex: Statistics and Geometry. , 1991 .

[12]  Prof. Dr. Valentino Braitenberg,et al.  Anatomy of the Cortex , 1991, Studies of Brain Function.

[13]  M. Abeles.  Local Cortical Circuits: An Electrophysiological Study , 1982 .

[14]  W. Singer,et al.  Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[15]  H Preißl,et al.  Dynamics of activity and connectivity in physiological neuronal networks , 1991 .

[16]  Günther Palm,et al.  Associative Networks and Cell Assemblies , 1986 .

[17]  Günther Palm,et al.  On Associative Memories , 1987 .

[18]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

[19]  D. O. Hebb,et al.  The organization of behavior , 1988 .

[20]  Roland Heim,et al.  Theoretical Approaches to Complex Systems , 1978 .

[21]  Michael Erb,et al.  Functional connectivity in neuronal systems: Context-dependence of effective network organization does not require synaptic plasticity , 1989 .

[22]  E. Vaadia,et al.  Firing patterns of single units in the prefrontal cortex and neural network models , 1990 .

[23]  Gèunther Palm,et al.  Neural Assemblies: An Alternative Approach to Artificial Intelligence , 1982 .

[24]  Nava Rubin,et al.  Neural networks with low local firing rates , 1989 .

[25]  E Ahissar,et al.  Neural interactions in the frontal cortex of a behaving monkey: signs of dependence on stimulus context and behavioral state. , 1991, Journal fur Hirnforschung.

[26]  Sompolinsky,et al.  Willshaw model: Associative memory with sparse coding and low firing rates. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[27]  Michael Erb,et al.  Stability in Physiology-Oriented Neuronal Network Models , 1990 .

[28]  A. Aertsen,et al.  Neuronal assemblies , 1989, IEEE Transactions on Biomedical Engineering.

[29]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[30]  S. Levin.  Lectu re Notes in Biomathematics , 1983 .

[31]  A. Aertsen,et al.  Dynamic Aspects of Neuronal Cooperativity: Fast Stimulus-Locked Modulations of Effective Connectivity , 1991 .