Recurrence and LaSalle invariance principle

2016 ◽  
Vol 93 ◽  
pp. 64-68 ◽  
Author(s):  
Boyang Ding ◽  
Changming Ding
2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Bo Liu ◽  
Shuang Li ◽  
Xuhui Tang

This paper investigates the second-order synchronization of two heterogeneous nonlinear coupled networks by introducing controller and adaptive laws. Based on Lyapunov stability properties and LaSalle invariance principle, it is proved that the position and the velocity of two heterogeneous nonlinear coupled networks are asymptotically stable. Finally, some numerical simulations are presented to verify the analytical results.


2021 ◽  
Vol 41 (1) ◽  
pp. 41-61
Author(s):  
Saiful Islam ◽  
Chandra Nath Podder

In this paper, a deterministic model for the dynamics of chikungunya virus transmission is formulated and analyzed. It is shown that the model has a disease free equilibrium (DFE) and by using the basic reprodution number (R0) local stability of DFE is proved when  R0 < 1. Also, the global stability of DFE is investigated by Lyapunov function and LaSalle Invariance Principle. We show that there exists a unique endemic equilibrium (EE) of the model which is locally asymptotically stable whenever R0 > 1 and establish the global stability of the EE when R0 > 1, by using Lyapunov function and LaSalle Invariance Principle for a special case. Numerical simulations and sensitivity analysis show that the destruction of breeding sites and reduction of average life spans of vector would be effective prevention to control the outbreak. Controlling of effective contact rates and reducing transmissions probabilities may reduce the disease prevalence. GANITJ. Bangladesh Math. Soc.41.1 (2021) 41-61


2021 ◽  
pp. 1-18
Author(s):  
CHRISTOPHE GALLESCO ◽  
DANIEL Y. TAKAHASHI

Abstract Mixing rates, relaxation rates, and decay of correlations for dynamics defined by potentials with summable variations are well understood, but little is known for non-summable variations. This paper exhibits upper bounds for these quantities for dynamics defined by potentials with square-summable variations. We obtain these bounds as corollaries of a new block coupling inequality between pairs of dynamics starting with different histories. As applications of our results, we prove a new weak invariance principle and a Hoeffding-type inequality.


2018 ◽  
Vol 10 (3) ◽  
pp. 1-37
Author(s):  
Yuval Filmus ◽  
Guy Kindler ◽  
Elchanan Mossel ◽  
Karl Wimmer
Keyword(s):  

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