Abstract
Dynamics of neural fields are tools used in neurosciences to understand the activities generated by large ensembles of neurons. They are also used in networks analysis and neuroinformatics in particular to model a continuum of neural networks. They are mathematical models that describe the average behavior of these congregations of neurons, which are often in large numbers, even in small cortexes of the brain. Therefore, change of average activity (potential, connectivity, firing rate, etc.) are described using systems of partial different equations. In their continuous or discrete forms, these systems have a rich array of properties, among which is the existence of nontrivial stationary solutions. In this paper, we propose an estimator for nontrivial solutions of dynamical neural fields with a single layer. The estimator is shown to be consistent and a computational algorithm is proposed to help carry out implementation. An illustrations of this consistency is given based on different inputs functions, different kernels, and different pulse emission rate functions.
Highlights
It is known that any small piece of human or animal cortex contains a vast number of neurons
There have been applications and extensions of his work in several directions and the birth of the field of dynamic field theory as byproduct. These extensions have for instance enabled analyses of electroencephalograms [4], shortterm memory [5], visual hallucinations [6,7], and most recently robotics using dynamics neural fields
Applications to robotics has proven very effective, as shown, for instance, by the works of Bicho, Mallet, and Schöner [8], Erlhangen and Bicho [9], Erlhangen and Schoner [10], and Bicho, Louro, and Erlhagen [11]. The authors of the latter provided studies in which robots to humans interactions were implemented based on information from Dynamic Neural Fields (DNF)
Summary
It is known that any small piece of human or animal cortex contains a vast number of neurons. Applications to robotics has proven very effective, as shown, for instance, by the works of Bicho, Mallet, and Schöner [8], Erlhangen and Bicho [9], Erlhangen and Schoner [10], and Bicho, Louro, and Erlhagen [11] The authors of the latter provided studies in which robots to humans interactions were implemented based on information from Dynamic Neural Fields (DNF). The tools of discrete dynamical systems can be applied non only to single-layer DNFs and to multiple-layers DNFs, where conditions for stability are well-known Another interesting aspect of DNFs is that, if we restrict Ω to the unit circle T where T = {z ∈ C : |z| = 1}, solutions may exist in the complex unit disk D =.
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