In this paper, we shall consider the global structure of positive bounded systems on the plane which have m singular points, but not any closed orbits and singular closed orbits. We shall prove that these systems have at least m Γ 1 connecting orbits; and all the connecting orbits, homoclinic orbits
Global properties for a class of dynamical neural circuits
β Scribed by Yuguang Fang; Thomas G. Kincaid
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 770 KB
- Volume
- 335
- Category
- Article
- ISSN
- 0016-0032
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β¦ Synopsis
In th& paper, we study the global properties of a class of asymmetrical Hopfield-type neural circuits. We first present a result for the existence and uniqueness of an equilibrium point; this result does not assume smoothness of the neural activation functions. Then we give some testable sufficient conditions for the global stability of such neural circuits. These results generalize a few previous known results and remove some restrictions on the neural circuits.
π SIMILAR VOLUMES
We consider a class of systems of differential equations in Nn which exhibits convergent dynamics. We find a Lyapunov function and show that every bounded trajectory converges to the set of equilibria. Our result generalizes the results of Cohen and Grossberg (1983) for convergent neural networks. I