scholarly journals Sufficient and necessary conditions for global attractivity and stability of a class of discrete Hopfield-type neural networks with time delays

2019 ◽  
Vol 16 (5) ◽  
pp. 4936-4946
Author(s):  
Yanjie Hong ◽  
◽  
Wanbiao Ma ◽  
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Global Attractivity ◽  
Necessary Conditions ◽  
Sufficient And Necessary Conditions

scholarly journals Global Behaviors of a Chemostat Model with Delayed Nutrient Recycling and Periodically Pulsed Input

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Kai Wang ◽  
Zhidong Teng ◽  
Fengqin Zhang
Keyword(s):  
Function Method ◽  
Global Attractivity ◽  
Necessary Conditions ◽  
Nutrient Recycling ◽  
Liapunov Function ◽  
Sufficient Condition ◽  
Chemostat Model ◽  
Dynamic Behaviors ◽  
Analysis Technique ◽  
Sufficient And Necessary Conditions

The dynamic behaviors in a chemostat model with delayed nutrient recycling and periodically pulsed input are studied. By introducing new analysis technique, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the model is established. Finally, an example is given to demonstrate the effectiveness of the results in this paper.

TWO PATCHES IMPULSIVE DIFFUSION PERIODIC SINGLE-SPECIES LOGISTIC MODEL

2010 ◽  
Vol 03 (01) ◽  
pp. 127-141 ◽  
Author(s):  
ZIJIAN LIU ◽  
ZHIDONG TENG ◽  
LONG ZHANG
Keyword(s):  
Periodic Solution ◽  
Iterative Method ◽  
Numerical Simulations ◽  
Logistic Model ◽  
Global Attractivity ◽  
Necessary Conditions ◽  
Positive Periodic Solution ◽  
Single Species ◽  
Impulsive Diffusion ◽  
Sufficient And Necessary Conditions

In this paper, we study a periodic single-species logistic system with impulsive diffusion in two patches. By using the iterative method, sufficient and necessary conditions on the existence, uniqueness and global attractivity of positive periodic solution and the extinction of species for this system are established. Two examples and numerical simulations are presented to illustrate the feasibility of our results.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

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