Global Stability Results

1993 ◽  
pp. 27-54 ◽  
Author(s):  
V. L. Kocic ◽  
G. Ladas
Keyword(s):  
Global Stability ◽  
Stability Results

scholarly journals On Some Sufficiency-Type Global Stability Results for Time-Varying Dynamic Systems with State-Dependent Parameterizations

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
M. De la Sen
Keyword(s):  
Global Stability ◽  
Dynamic Systems ◽  
Taylor Series Expansion ◽  
Time Varying ◽  
State Dependent ◽  
The Matrix ◽  
The Stability ◽  
Interval Type ◽  
Truncation Order ◽  
Stability Results

This paper formulates sufficiency-type global stability and asymptotic stability results for, in general, nonlinear time-varying dynamic systems with state-trajectory solution-dependent parameterizations. The stability proofs are based on obtaining sufficiency-type conditions which guarantee that either the norms of the solution trajectory or alternative interval-type integrals of the matrix of dynamics of the higher-order than linear terms do not grow faster than their available supremum on the preceding time intervals. Some extensions are also given based on the use of a truncated Taylor series expansion of chosen truncation order with multiargument integral remainder for the dynamics of the differential system.

scholarly journals Comment on “Transmission Model of Hepatitis B Virus with Migration Effect”

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Anwar Zeb ◽  
Gul Zaman
Keyword(s):  
Mathematical Biology ◽  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Global Stability ◽  
Recent Literature ◽  
Transmission Model ◽  
Reproductive Number ◽  
Migration Effect ◽  
B Virus ◽  
Stability Results

We show the erroneous assumptions and reasoning by introducing the migration effect of individuals in the transmission model of Hepatitis B virus. First, some false results related to the eigenvalues and reproductive number in the recent literature in mathematical biology will be presented. Then, it will be proved that the product of the matrices in the next generation method to obtain the reproductive numberR0is not correct and the local and global stability results based on the reproductive numberR0are considered false.

Global stability results for temperature modulated convection in ferrofluids

2013 ◽  
Vol 219 (11) ◽  
pp. 6204-6211 ◽  
Author(s):  
Jitender Singh ◽  
Evor Hines ◽  
Daciana Iliescu
Keyword(s):  
Global Stability ◽  
Stability Results
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