Motivation in action: A process model of L2 motivation

As part of a long-term project aimed at designing classroom interventions to motivate language learners, we have searched for a motivation model that could serve as a theoretical basis for the methodological applications. We have found that none of the existing models we considered were entirely adequate for our purpose for three reasons: (1) they did not provide a sufficiently comprehensive and detailed summary of all the relevant motivational influences on classroom behaviour; (2) they tended to focus on how and why people choose certain courses of action, while ignoring or playing down the importance of motivational sources of executing goal-directed behaviour; and (3) they did not do justice to the fact that motivation is not static but dynamically evolving and changing in time, making it necessary for motivation constructs to contain a featured temporal axis. Consequently, partly inspired by Heckhausen and Kuhl's 'Action Control Theory', we have developed a new 'Process Model of L2 Motivation', which is intended both to account for the dynamics of motivational change in time and to synthesise many of the most important motivational conceptualisations to date. In this paper we describe the main components of this model, also listing a number of its limitations which need to be resolved in future research.

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).