Title :
Flow invariance for competitive multi-modal neural networks
Author :
Meyer-Bäse, Anke ; Pilyugin, Sergei S.
Author_Institution :
Dept. of Electr. & Comput. Eng., Florida State Univ., Tallahassee, FL, USA
Abstract :
We present a new method of analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance. We are able to show the conditions under which the solutions of such a system are bounded being less restrictive than with the K-monotone theory, singular perturbation theory, or those based on supervised synaptic learning. We prove the existence and the uniqueness of the equilibrium. A strict Lyapunov function for the flow of a competitive neural system with different time scales is given and based on it we are able to prove the global exponential stability of the equilibrium point.
Keywords :
Lyapunov methods; asymptotic stability; neural nets; biological relevant system; competitive multimodal neural networks; competitive neural system; equilibrium point; flow invariance; global exponential stability; strict Lyapunov function; Biological neural networks; Equations; Feedforward neural networks; Mathematics; Multi-layer neural network; Neural networks; Neurofeedback; Neurons; Robust stability; Supervised learning;
Conference_Titel :
Neural Networks, 2003. Proceedings of the International Joint Conference on
Print_ISBN :
0-7803-7898-9
DOI :
10.1109/IJCNN.2003.1224067
