A biologically based competition model for self-organizing neural networks

This work presents the design of an unsupervised neural network system, CSNN (competitive self-organizing neural network), for pattern recognition and classification. The CSNN model is based on a system of ordinary differential equations, motivated by Volterra and Lotka´s models of interacting species in biology. The CSNN features a continuous time system dynamics that is free of auxiliary control mechanisms, complex hard threshold switching functions, or LUT based approaches found in conventional pattern processing. These characteristics are essential for establishing self-organizing properties in unsupervised nets. Due to inherent complexities, attempts to analyze properties and capabilities of this system for pattern processing still remains a challenging task. Research rarely extends beyond the study of system stability, and other issues are essential for characterizing system properties and solution curves of their dynamics. The paper develops a self-organizing scheme for unsupervised neural networks, whose self-organizing properties are implicitly coded within a trajectory structure defined only by ordinary differential equations. The dynamic behavior is well understood and characterized using only the conventional analytical tools in mathematics. The constructed dynamics realizes a fixed finite set of equilibria in any fixed finite dimensional space. The ω-limit set of all trajectories initiated in its state space is the union of the stored pattern categories, represented as asymptotically stable limit points