scholarly journals Discrete three-stage population model: persistence and global stability results

2008 ◽  
Vol 2 (4) ◽  
pp. 415-427 ◽  
Author(s):  
Azmy S. Ackleh ◽  
Patrick De Leenheer
Keyword(s):  
Global Stability ◽  
Population Model ◽  
Stability Results ◽  
Model Persistence

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.

GLOBAL STABILITY OF A NONLINEAR DISCRETE POPULATION MODEL WITH TIME DELAYS

2007 ◽  
Vol 10 (03) ◽  
pp. 315-333
Author(s):  
NA FANG ◽  
XIAOXING CHEN
Keyword(s):  
Global Stability ◽  
Positive Solution ◽  
Positive Solutions ◽  
Population Model ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Type ◽  
Discrete Population ◽  
Liapunov Functionals ◽  
Discrete Population Model

The global stability of a nonlinear discrete population model of Volterra type is studied. The model incorporates time delays. By linearization of the model at positive solutions and construction of Liapunov functionals, sufficient conditions are obtained to ensure that a positive solution of the model is stable and attracts all positive solutions. An example shows the feasibility of our main results.

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