scholarly journals Global stability conditions for three-dimensional Lotka-Volterra systems

1994 ◽  
Vol 7 (3) ◽  
pp. 67-71 ◽  
Author(s):  
Z.-Y. Lu ◽  
Y. Takeuchi
Keyword(s):  
Global Stability ◽  
Three Dimensional ◽  
Stability Conditions ◽  
Volterra Systems

scholarly journals Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey

Diversity ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 23
Author(s):  
Jawdat Alebraheem
Keyword(s):  
Global Stability ◽  
Stability Conditions ◽  
Dynamic Behaviors ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Predator Prey Model ◽  
Prey Model ◽  
Proposed Model

In this article, the use of predator-dependent functional and numerical responses is proposed to form an autonomous predator–prey model. The dynamic behaviors of this model were analytically studied. The boundedness of the proposed model was proven; then, the Kolmogorov analysis was used for validating and identifying the coexistence and extinction conditions of the model. In addition, the local and global stability conditions of the model were determined. Moreover, a novel idea was introduced by adding the oscillation of the immigration of the prey into the model which forms a non-autonomous model. The numerically obtained results display that the dynamic behaviors of the model exhibit increasingly stable fluctuations and an increased likelihood of coexistence compared to the autonomous model.

scholarly journals Improved global stability condition analysis for time-delay fast active queue management scalable transmission control protocol

2019 ◽  
Vol 15 (5) ◽  
pp. 155014771985193
Author(s):  
Jinfeng Huang ◽  
Lingjing Zeng ◽  
Xiaolong Chen
Keyword(s):  
Time Delay ◽  
Global Stability ◽  
Transmission Control Protocol ◽  
Active Queue Management ◽  
Maximum Growth ◽  
Stability Conditions ◽  
Queue Management ◽  
Transmission Control ◽  
Delay Term ◽  
Control Protocol

The nonlinear time-delay fast active queue management scalable transmission control protocol model was studied in this article. By analyzing the boundedness properties for solution trajectory of the fast active queue management scalable transmission control protocol model, the iterative relations of fast active queue management scalable transmission control protocol trajectory bounds were obtained. Furthermore, we calculated the maximum growth direction of the delay term in the integral interval and applied the backward method to calculate the lower conservative bound corresponding to each time of the delay term. Therefore, the global stability parameter condition of fast active queue management scalable transmission control protocol, which was less conservative than the existing global stability conditions, was obtained in this article. The validity of the stability conditions obtained in this article was verified by NS-2 simulation experiment.

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