Synchronous and Asynchronous 2 Evaluation of Dynamic Neural Fields

6 In [26], we've introduced a dynamic model of visual attention based on the Continuum Neural 7 Field Theory [29] that explained attention as being an emergent property of a dynamic neural 8 field. The fundamental property of the model is its facility to select a single stimulus out 9 of several perfectly identical input stimuli by applying asynchronous computation. In the 10 absence of external noise and with a zero initial state, the theoretical mathematical solution 11 of the field equation predicts the final equilibrium state to equally represent all of the input 12 stimuli. This finding is valid for synchronous numerical computation of the system dynamics 13 where elements of the spatial field are computed all together at each time point. However, 14 asynchronous computation, where elements of the spatial field are iterated in time one after 15 the other yields different results leading the field to move towards a single stable input pattern. 16 This behavior is in fact quite similar to the effect of noise on dynamic fields. The present work 17 aims at studying this phenomenom in some details and characterizes the relation between 18 noise, synchronous evaluation (the " regular " mathematical integration) and asynchronous 19 evaluation in the case of a simple dual particle system. More generally, we aim at explaining 20 the behavior of a general differential equation system when it is considered as a set of particles 21 that may or may not iterated by synchronous computations.