Bifurcation study of phase oscillator systems with attractive and repulsive interaction.

We study a model of globally coupled phase oscillators that contains two groups of oscillators with positive (synchronizing) and negative (desynchronizing) incoming connections for the first and second groups, respectively. This model was previously studied by Hong and Strogatz (the Hong-Strogatz model) in the case of a large number of oscillators. We consider a generalized Hong-Strogatz model with a constant phase shift in coupling. Our approach is based on the study of invariant manifolds and bifurcation analysis of the system. In the case of zero phase shift, various invariant manifolds are analytically described and a new dynamical mode is found. In the case of a nonzero phase shift we obtained a set of bifurcation diagrams for various systems with three or four oscillators. It is shown that in these cases system dynamics can be complex enough and include multistability and chaotic oscillations

Winner-take-all in a phase oscillator system with adaptation.

We consider a system of generalized phase oscillators with a central element and radial connections. In contrast to conventional phase oscillators of the Kuramoto type, the dynamic variables in our system include not only the phase of each oscillator but also the natural frequency of the central oscillator, and the connection strengths from the peripheral oscillators to the central oscillator. With appropriate parameter values the system demonstrates winner-take-all behavior in terms of the competition between peripheral oscillators for the synchronization with the central oscillator. Conditions for the winner-take-all regime are derived for stationary and non-stationary types of system dynamics. Bifurcation analysis of the transition from stationary to non-stationary winner-take-all dynamics is presented. A new bifurcation type called a Saddle Node on Invariant Torus (SNIT) bifurcation was observed and is described in detail. Computer simulations of the system allow an optimal choice of parameters for winner-take-all implementation

Reaction times in visual search can be explained by a simple model of neural synchronization

publisher: Elsevier articletitle: Reaction times in visual search can be explained by a simple model of neural synchronization journaltitle: Neural Networks articlelink: http://dx.doi.org/10.1016/j.neunet.2016.12.003 content_type: article copyright: © 2016 Elsevier Ltd. All rights reserved

EEG Correlates of Attentional Load during Multiple Object Tracking

While human subjects tracked a subset of ten identical, randomly-moving objects, event-related potentials (ERPs) were evoked at parieto-occipital sites by task-irrelevant flashes that were superimposed on either tracked (Target) or non-tracked (Distractor) objects. With ERPs as markers of attention, we investigated how allocation of attention varied with tracking load, that is, with the number of objects that were tracked. Flashes on Target discs elicited stronger ERPs than did flashes on Distractor discs; ERP amplitude (0–250 ms) decreased monotonically as load increased from two to three to four (of ten) discs. Amplitude decreased more rapidly for Target discs than Distractor discs. As a result, with increasing tracking loads, the difference between ERPs to Targets and Distractors diminished. This change in ERP amplitudes with load accords well with behavioral performance, suggesting that successful tracking depends upon the relationship between the neural signals associated with attended and non-attended objects

A computational model of familiarity detection for natural pictures, abstract images, and random patterns: Combination of deep learning and anti-Hebbian training

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordWe present a neural network model for familiarity recognition of different types of images in the perirhinal cortex (the FaRe model). The model is designed as a two-stage system. At the first stage, the parameters of an image are extracted by a pretrained deep learning convolutional neural network. At the second stage, a two-layer feed forward neural network with anti-Hebbian learning is used to make the decision about the familiarity of the image. FaRe model simulations demonstrate high capacity of familiarity recognition memory for natural pictures and low capacity for both abstract images and random patterns. These findings are in agreement with psychological experiments