Proving Asymptotic Stability with LaSalle’s Invariance Principle: On the Automatic Computation of Invariant Sets Using Quantifier Elimination*

2020 ◽  
Author(s):  
Daniel Gerbet ◽  
Klaus Robenack
Keyword(s):  
Asymptotic Stability ◽  
Invariance Principle ◽  
Quantifier Elimination ◽  
Invariant Sets ◽  
Lasalle’S Invariance Principle ◽  
Automatic Computation ◽  
Lasalle's Invariance Principle

GLOBAL STABILITY FOR A PHYTOPLANKTON-NUTRIENT SYSTEM

2000 ◽  
Vol 08 (02) ◽  
pp. 195-209 ◽  
Author(s):  
OLIVIER PARDO
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Global Stability ◽  
Invariance Principle ◽  
Global Asymptotic Stability ◽  
Lasalle’S Invariance Principle ◽  
Bacterial Decomposition ◽  
Autonomous Differential Equations ◽  
Lasalle's Invariance Principle

The model proposed by A. H. Taylor et al. [18] is discussed, with a view to determining the global asymptotic stability of the equilibria. The system consists of two autonomous differential equations, modeling the couple Phytoplankton-Nutrient with no delay on the recycling efficiency of nutrient by bacterial decomposition. Two distinct cases, persistence and extinction of phytoplankton are considered. In each case we will state the local and then the global stability of the equilibria by constructing an appropriate Lyapunov function and using the LaSalle's invariance principle. Also, in the case of extinction of phytoplankton we have introduced a supply of nutrient in the system and we have revealed the bloom of phytoplankton, which appears biologically in upwelling conditions.

SYNCHRONOUS AND ASYNCHRONOUS BRAIN-STATE-IN-A-BOX INFORMATION SYSTEM NEURAL MODELS

1999 ◽  
Vol 09 (01) ◽  
pp. 61-74 ◽  
Author(s):  
HUBERT Y. CHAN ◽  
STEFEN HUI ◽  
STANISLAW H. ŻAK
Keyword(s):  
Information System ◽  
United Nations ◽  
Invariance Principle ◽  
Brain State ◽  
Neural Models ◽  
Lasalle’S Invariance Principle ◽  
The United Nations ◽  
The Stability ◽  
Lasalle's Invariance Principle

Synchronous and asynchronous information system neural models are proposed that are hybrids of Pawlak's information system and Brain-State-in-a-Box (BSB) neural models. The stability of the proposed models is studied using LaSalle's Invariance Principle. Applications to an analysis of the United Nations activities are presented as examples.

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