Generalization of a flow-invariance criterion

2017 ◽  
Author(s):  
Octavian Pastravanu ◽  
Mihaela-Hanako Matcovschi ◽  
Mihail Voicu
Keyword(s):  
Flow Invariance

GLOBAL ASYMPTOTIC STABILITY OF A CLASS OF DYNAMICAL NEURAL NETWORKS

2003 ◽  
Vol 13 (01) ◽  
pp. 47-53 ◽  
Author(s):  
ANKE MEYER-BÄSE ◽  
SERGEI S. PILYUGIN
Keyword(s):  
Short Term Memory ◽  
Neural System ◽  
Short Term ◽  
Slow Dynamic ◽  
Biologically Relevant ◽  
Synaptic Modification ◽  
Slow Part ◽  
Flow Invariance ◽  
Dynamical Neural Networks ◽  
Dynamic Variables

The dynamics of cortical cognitive maps developed by self–organization must include the aspects of long and short–term memory. The behavior of the network is such characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural biologically relevant system. We present new stability conditions for analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance. We prove the existence and uniqueness of the equilibrium, and give a quadratic–type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables and thus prove the global stability of the equilibrium point.

scholarly journals Tangent vectors to sets in the theory of geodesics

1987 ◽  
Vol 106 ◽  
pp. 29-47 ◽  
Author(s):  
Dumitru Motreanu
Keyword(s):  
Closed Subset ◽  
Tangent Vector ◽  
General Concept ◽  
Recent Book ◽  
Closed Sets ◽  
Banach Manifolds ◽  
Flow Invariance ◽  
Tangent Vectors

In the setting of Banach manifolds the notion of tangent vector to an arbitrary closed subset has been introduced in [11] by the author and N. H. Pavel, and it has been used in flow-invariance and optimization ([11], [12], [13]). For detailed informations on tangent vectors to closed sets (including historical comments) we refer to the recent book of N. H. Pavel [17].The aim of this paper is to apply this general concept of tangency in the study of geodesies. We are concerned with geodesies which have either the endpoints in given closed subsets or the same angle for a fixed closed subset. This approach allows one to extend important results due to K. Grove [4] and T. Kurogi ([6], [7]).

scholarly journals Generalized flow invariance for differential inclusions

2006 ◽  
Vol 2006 ◽  
pp. 1-7
Author(s):  
T. Gnana Bhaskar ◽  
V. Lakshmikantham
Keyword(s):  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Strong Invariance ◽  
Flow Invariance ◽  
Proximal Normals ◽  
Proximal Aiming

We introduce a generalized notion of invariance for differential inclusions, using a proximal aiming condition in terms of proximal normals. A set of sufficient conditions for the weak and strong invariance in the generalized sense are presented.

scholarly journals Flow Invariance on Stratified Domains

2013 ◽  
Vol 21 (2) ◽  
pp. 377-403 ◽  
Author(s):  
Richard C. Barnard ◽  
Peter R. Wolenski
Keyword(s):  
Flow Invariance
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