This paper studies the eeect of slow cyclic variation of parameters on the phase of the oscillating Morris-Lecar model. In chemical oscillators it is known that a phase shift, called the geometric phase shift, is observed upon return to an initial point in parameter space. We nd geometric phase shifts for a two-parameter variation in the Morris-Lecar model. As with the chemical oscillator, the ...

David Terman Department of Mathematics The Ohio State University Columbus, Ohio 43210, USA [email protected] An novel class of locally excitatory, globally inhibitory oscillator networks is proposed. The model of each oscillator corresponds to a standard relaxation oscillator with two time scales. The network exhibits a mechanism of selective gating, whereby an oscillator jumping up to...

In this paper, a dynamically coupled neural oscillator network is proposed for image segmentation. Instead of pair-wise coupling, an ensemble of oscillators coupled in a local region is used for grouping. We introduce a set of neighborhoods to generate dynamical coupling structures associated with a specific oscillator. Based on the proximity and similarity principles, two grouping rules are pr...

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction assumption may well n...

In this paper, we derive the minimum-energy periodic control that entrains an ensemble of structurally similar neural oscillators to a desired frequency. The state-space representation of a nominal oscillator is reduced to a phase model by computing its limit cycle and phase response curve, from which the optimal control is derived by using formal averaging and the calculus of variations. We fo...

We analyze the dynamics of the neural circuit of the lamprey central pattern generator. This analysis provides insight into how neural interactions form oscillators and enable spontaneous oscillations in a network of damped oscillators, which were not apparent in previous simulations or abstract phase oscillator models. We also show how the different behavior regimes (characterized by phase and...

Neural oscillatory dynamics are a candidate mechanism to steer perception of time and temporal rate change. While oscillator models of time perception are strongly supported by behavioral evidence, a direct link to neural oscillations and oscillatory entrainment has not yet been provided. In addition, it has thus far remained unaddressed how context-induced illusory percepts of time are coded f...

We study the reliability of large networks of coupled neural oscillators in response to fluctuating stimuli. Reliability means that a stimulus elicits essentially identical responses upon repeated presentations. We view the problem on two scales: neuronal reliability, which concerns the repeatability of spike times of individual neurons embedded within a network, and pooled-response reliability...