Recurrence and LaSalle invariance principle

2016 ◽  
Vol 93 ◽  
pp. 64-68 ◽  
Author(s):  
Boyang Ding ◽  
Changming Ding
Keyword(s):  
Invariance Principle ◽  
Lasalle Invariance Principle

scholarly journals Adaptive Second-Order Synchronization of Two Heterogeneous Nonlinear Coupled Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Bo Liu ◽  
Shuang Li ◽  
Xuhui Tang
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Invariance Principle ◽  
Second Order ◽  
Asymptotically Stable ◽  
Stability Properties ◽  
Analytical Results ◽  
Lasalle Invariance Principle ◽  
Coupled Networks ◽  
Adaptive Laws

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.

scholarly journals A mathematical analysis of the dynamics of chikungunya virus transmission

2021 ◽  
Vol 41 (1) ◽  
pp. 41-61
Author(s):  
Saiful Islam ◽  
Chandra Nath Podder
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Invariance Principle ◽  
Chikungunya Virus ◽  
Deterministic Model ◽  
Virus Transmission ◽  
Effective Prevention ◽  
Breeding Sites ◽  
Lasalle Invariance Principle ◽  
Effective Contact

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

scholarly journals Mixing rates for potentials of non-summable variations

2021 ◽  
pp. 1-18
Author(s):  
CHRISTOPHE GALLESCO ◽  
DANIEL Y. TAKAHASHI
Keyword(s):  
Invariance Principle ◽  
Type Inequality ◽  
Upper Bounds ◽  
Decay Of Correlations ◽  
Relaxation Rates ◽  
Weak Invariance Principle ◽  
Weak Invariance ◽  
Coupling Inequality ◽  
Mixing Rates

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.

scholarly journals Invariance Principle on the Slice

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