Self-organized topological structures in neural networks for the visual cortex of the brain

Abstract Expressed layered structures in the cerebral and cerebellar cortices of the brain are attributed to most animals while the human and some primate neostriatum neurons are laid out as clustered higher and lower cell density mosaics. These ordered structures are probably formed by a self-organizing mechanism which is widely discussed in the present paper. We use the notation “Self-organizing” not as a self-learning or self-mapping algorithm, widespread in a neural network learning paradigm, but as a principle studying physical nonequilibrium mechanisms. Considering the theoretical principle based on neural networks, an N-shaped current–voltage relation was included in the model and its influence on the stability and conditions of self-organization examined. The formation of ordered structures was founded in the vicinity of the equilibrium point. Based on the group and bifurcation theories, the self-organized topological structures were grounded for the visual cortex. Concomitant computational experiments with wide illustrations of the ordered structures—patterns—are presented. The experimentally registered ordered structures and computational ones have been roughly compared.