Establishment of topological maps — a model study

We consider a model, proposed in 1], mimicking the self-organization between the tectum and the retina and being capable of establishing the topological maps. By performing the saturated attractor analysis 2, 3, 4], we first give the parameter region of the dynamics in which a specific configuration is an attractor of the dynamics. We prove that a parameter region in which only the topological map is an attractor of the dynamics does not exist. However by a reasonable and slight modification of the model, the existence of a parameter gap for the topological map is verified, which implies that the development of the topological maps in the modified model is independent of the initial value.