We study bi-Lyapunov stable homoclinic classes for a C^(1)generic flow on a closed Rieman-nian manifold and prove that such a homoclinic class contains no singularity.This enables a parallel study of bi-Lyapunov stabl...We study bi-Lyapunov stable homoclinic classes for a C^(1)generic flow on a closed Rieman-nian manifold and prove that such a homoclinic class contains no singularity.This enables a parallel study of bi-Lyapunov stable dynamics for flows and for diffeomorphisms.For example,we can then show tha t a bi-Lyapunov st able homoclinic class for a C^(1)generic flow is hyperbolic if and only if all periodic orbits in the class have the same stable index.展开更多
In this paper, a fuzzy operator of max-product is defined at first, and the fuzzy bi-directional associative memory (FBAM) based on the fuzzy operator of max-product is given. Then the properties and the Lyapunov stab...In this paper, a fuzzy operator of max-product is defined at first, and the fuzzy bi-directional associative memory (FBAM) based on the fuzzy operator of max-product is given. Then the properties and the Lyapunov stability of equilibriums of the networks are studied.展开更多
Discrete-time version of the bi-directional Cohen-Grossberg neural network is stud-ied in this paper. Some sufficient conditions are obtained to ensure the global exponen-tial stability of such networks with discrete ...Discrete-time version of the bi-directional Cohen-Grossberg neural network is stud-ied in this paper. Some sufficient conditions are obtained to ensure the global exponen-tial stability of such networks with discrete time based on Lyapunov method. These results do not require the symmetry of the connection matrix and the monotonicity, boundedness and differentiability of the activation function.展开更多
文摘We study bi-Lyapunov stable homoclinic classes for a C^(1)generic flow on a closed Rieman-nian manifold and prove that such a homoclinic class contains no singularity.This enables a parallel study of bi-Lyapunov stable dynamics for flows and for diffeomorphisms.For example,we can then show tha t a bi-Lyapunov st able homoclinic class for a C^(1)generic flow is hyperbolic if and only if all periodic orbits in the class have the same stable index.
文摘In this paper, a fuzzy operator of max-product is defined at first, and the fuzzy bi-directional associative memory (FBAM) based on the fuzzy operator of max-product is given. Then the properties and the Lyapunov stability of equilibriums of the networks are studied.
基金supported by Scientific Research Foundation of Hunan Provincial EducationDepartment (04A055, 05A057,03C009)
文摘Discrete-time version of the bi-directional Cohen-Grossberg neural network is stud-ied in this paper. Some sufficient conditions are obtained to ensure the global exponen-tial stability of such networks with discrete time based on Lyapunov method. These results do not require the symmetry of the connection matrix and the monotonicity, boundedness and differentiability of the activation function.
