10 research outputs found
Analyzing Stability of Equilibrium Points in Neural Networks: A General Approach
Networks of coupled neural systems represent an important class of models in
computational neuroscience. In some applications it is required that
equilibrium points in these networks remain stable under parameter variations.
Here we present a general methodology to yield explicit constraints on the
coupling strengths to ensure the stability of the equilibrium point. Two models
of coupled excitatory-inhibitory oscillators are used to illustrate the
approach.Comment: 20 pages, 4 figure
Short term synaptic depression improves information transfer in perceptual multistability
Competitive neural networks are often used to model the dynamics of
perceptual bistability. Switching between percepts can occur through
fluctuations and/or a slow adaptive process. Here, we analyze switching
statistics in competitive networks with short term synaptic depression and
noise. We start by analyzing a ring model that yields spatially structured
solutions and complement this with a study of a space-free network whose
populations are coupled with mutual inhibition. Dominance times arising from
depression driven switching can be approximated using a separation of
timescales in the ring and space-free model. For purely noise-driven switching,
we use energy arguments to justify how dominance times are exponentially
related to input strength. We also show that a combination of depression and
noise generates realistic distributions of dominance times. Unimodal functions
of dominance times are more easily differentiated from one another using
Bayesian sampling, suggesting synaptic depression induced switching transfers
more information about stimuli than noise-driven switching. Finally, we analyze
a competitive network model of perceptual tristability, showing depression
generates a memory of previous percepts based on the ordering of percepts.Comment: 26 pages, 15 figure
Dynamical Analysis of DTNN with Impulsive Effect
We present dynamical analysis of discrete-time delayed neural networks with impulsive effect. Under impulsive effect, we derive some new criteria for the invariance and attractivity of discretetime neural networks by using decomposition approach and delay difference inequalities. Our results improve or extend the existing ones
Modelling and Contractivity of Neural-Synaptic Networks with Hebbian Learning
This paper is concerned with the modelling and analysis of two of the most
commonly used recurrent neural network models (i.e., Hopfield neural network
and firing-rate neural network) with dynamic recurrent connections undergoing
Hebbian learning rules. To capture the synaptic sparsity of neural circuits we
propose a low dimensional formulation. We then characterize certain key
dynamical properties. First, we give biologically-inspired forward invariance
results. Then, we give sufficient conditions for the non-Euclidean
contractivity of the models. Our contraction analysis leads to stability and
robustness of time-varying trajectories -- for networks with both excitatory
and inhibitory synapses governed by both Hebbian and anti-Hebbian rules. For
each model, we propose a contractivity test based upon biologically meaningful
quantities, e.g., neural and synaptic decay rate, maximum in-degree, and the
maximum synaptic strength. Then, we show that the models satisfy Dale's
Principle. Finally, we illustrate the effectiveness of our results via a
numerical example.Comment: 24 pages, 4 figure