We derive analytical expressions of local codimension-1 bifurcations for a fully connected, additive, discrete-time recurrent neural network (RNN), where we regard the external inputs as bifurcation parameters. The complexity of the bifurcation diagrams obtained increases exponentially with the number of neurons. We show that a three-neuron cascaded network can serve as a universal oscillator, ...

In this paper we present a neural oscillator model of stimulus response theory that exhibits quantum-like behavior. We then show that without adding any additional assumptions, a quantum model constructed to fit observable pairwise correlations has no predictive power over the unknown triple moment, obtainable through the activation of multiple oscillators. We compare this with the results obta...

This thesis considers a stochastic dynamical system that has multiple time scales. The focus lies on the planar slow-fast stochastic differential equation (a singularly perturbed stochastic system) modeling the spiking activity of an isolated FitzHugh-Nagumo neural oscillator. We analyze the model equation on the slow time scale τ (Eq.(1)) and on the fast time scale t (Eq.(2)). { dvτ = ε f(vτ ,...

An oscillatory neural network model is presented that allows selection of a specified object from the image. The processing of the image is divided into two stages. The first stage implements contour extraction by applying traditional image processing algorithms. The result is raw contours accompanied by the noise and some spurious objects. During the second stage the searched object is segment...

Although homeostatic mechanisms remain of utmost importance, rhythmic changes are present also. The main ones have a period of 24 h (circadian) or about 2-3 h (ultradian). Circadian rhythms are derived from a body clock, found in the base of the brain, and from the pattern of our sleep wake cycle, including activity and meal times. These rhythms promote the regular changes between an active wak...