Exotic dynamics in a firing rate model of neural tissue with threshold accommodation

Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognized that more realistic models of neural tissue can be obtained with the introduction of state-dependent dynamic thresholds. In this paper we treat a specific phenomenological model of threshold accommodation that mimics many of the properties originally described by Hill. Importantly we explore the consequences of this dynamic threshold at the tissue level, by modifying a standard neural field model of Wilson-Cowan type. As in the case without threshold accommodation classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps) in both one and two dimensions. Importantly an analysis of bump stability in one dimension, using recent Evans function techniques, shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. In the regime where a bump solution does not exist direct numerical simulations show the possibility of self-replicating bumps via a form of bump splitting. Simulations in two space dimensions show analogous localized and traveling solutions to those seen in one dimension. Indeed dynamical behavior in this neural model appears reminiscent of that seen in other dissipative systems that support localized structures, and in particular those of coupled cubic complex Ginzburg-Landau equations. Further numerical explorations illustrate that the traveling pulses in this model exhibit particle like properties, similar to those of dispersive solitons observed in some three component reaction-diffusion systems. A preliminary account of this work first appeared in S Coombes and M R Owen, Bumps, breathers, and waves in a neural network with spike frequency adaptation, Physical Review Letters 94 (2005), 148102(1-4).

Simulating customer experience and word-of-mouth in retail: a case study

Agents offer a new and exciting way of understanding the world of work. In this paper we describe the development of agent-based simulation models, designed to help to understand the relationship between people management practices and retail performance. We report on the current development of our simulation models which includes new features concerning the evolution of customers over time. To test the features we have conducted a series of experiments dealing with customer pool sizes, standard and noise reduction modes, and the spread of customers’ word of mouth. To validate and evaluate our model, we introduce new performance measure specific to retail operations. We show that by varying different parameters in our model we can simulate a range of customer experiences leading to significant differences in performance measures. Ultimately, we are interested in better understanding the impact of changes in staff behavior due to changes in store management practices. Our multi-disciplinary research team draws upon expertise from work psychologists and computer scientists. Despite the fact we are working within a relatively novel and complex domain, it is clear that intelligent agents offer potential for fostering sustainable organizational capabilities in the future.