Continuous attractors and attraction basins of a population decoding
model with a parameter as a switch
Abstract
This paper is concerned with continuous attractors and attraction basins
of a population decoding model with a parameter as a switch. Since an
attractor for a model is a equilibrium point of its phase space such
that for “many” choices of initial point the model will evolve towards
the point, the attractor belongs to the omega-limit sets of theses
initial points. Therefore, we can construct the mapping between initial
values and omega-limit sets to study the properties of attractors for
the model. In this article, firstly, the omega-limit set of each initial
value are obtained of the model, and the mapping between the initial
values and the omega-limit sets is successfully constructed by the
omega-limit set of each initial value for the model. Secondly, applying
this mapping, we not only obtain the attraction basin of each attractor
and the stability of these attractors, but also find a new sufficient
condition of nonzero continuous attractors of this model. Finally, we
get bifurcations can occur in which continuous attractors undergo
qualitative changes as the model parameter passes through a critical
bifurcation value.