In irreducible excitatory networks of analog graded-response neurons, the trajectories of most solutions tend to the equilibria. We derive sufficient conditions for such networks to be globally asymptotically stable. When the network possesses several locally stable equilibria, their location in the phase space is discussed and a description of their attraction basin is given. The results hold even when interunit transmission is delayed.
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Elife
August 2015
Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, United States.
Cortical spike trains often appear noisy, with the timing and number of spikes varying across repetitions of stimuli. Spiking variability can arise from internal (behavioral state, unreliable neurons, or chaotic dynamics in neural circuits) and external (uncontrolled behavior or sensory stimuli) sources. The amount of irreducible internal noise in spike trains, an important constraint on models of cortical networks, has been difficult to estimate, since behavior and brain state must be precisely controlled or tracked.
View Article and Find Full Text PDFNeuron
March 2008
Program in Neurobiology and Behavior, University of Washington, Seattle, WA 98195, USA.
Adaptation or gain control allows sensory neurons to encode diverse stimuli using a limited range of output signals. Rod vision exemplifies a general challenge facing adaptational mechanisms-balancing the benefits of averaging to create a reliable signal for adaptation with the need to adapt rapidly and locally. The synapse between rod bipolar and AII amacrine cells dominates adaptation at low light levels.
View Article and Find Full Text PDFIEEE Trans Neural Netw
June 2010
INSERM U. 444, Paris Cedex 12, France.
In irreducible excitatory networks of analog graded-response neurons, the trajectories of most solutions tend to the equilibria. We derive sufficient conditions for such networks to be globally asymptotically stable. When the network possesses several locally stable equilibria, their location in the phase space is discussed and a description of their attraction basin is given.
View Article and Find Full Text PDFNeural Comput
May 2007
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
We consider a fast-slow excitable system subject to a stochastic excitatory input train and show that under general conditions, its long-term behavior is captured by an irreducible Markov chain with a limiting distribution. This limiting distribution allows for the analytical calculation of the system's probability of firing in response to each input, the expected number of response failures between firings, and the distribution of slow variable values between firings. Moreover, using this approach, it is possible to understand why the system will not have a stationary distribution and why Monte Carlo simulations do not converge under certain conditions.
View Article and Find Full Text PDFBrain Cogn
May 1992
Department of Psychology, Monash University, Victoria Australia.
In his On the Functions of the Brain and Each of Its Parts, Franz Joseph Gall proposed that significant behaviors resulted from certain independent, irreducible, and fundamental faculties or propensities. There seems to be nothing in his system for explaining how two or more faculties interact, especially how one comes to predominate over another, other than the implicit notion that the stronger will be manifested. This peculiarity of Gall's system is consistent with the predominately "excitatory" physiology of his time in which there was no place for an independent inhibitory process.
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