Local stability analysis of TCP with a queue management policy: Single bottleneck link with two delays

Author(s):  
Sai Prasad ◽  
Gaurav Raina
Author(s):  
Yu Wang

Abstract A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.


2018 ◽  
Vol 28 (09) ◽  
pp. 1850116 ◽  
Author(s):  
A. M. Yousef ◽  
S. M. Salman ◽  
A. A. Elsadany

A discrete predator–prey model with delayed density dependence in the rate of growth of the prey is considered. In particular, we analyze the model presented by Kot [2005] which consists of three coupled difference equations and contains two parameters. Existence and local stability analysis of fixed points of the model are addressed. The normal form technique and perturbation method are applied to the different types of bifurcations that exist in the model being investigated. It is proved that the existence of transcritical and Neimark–Sacker bifurcations can occur in the model. In addition, the chaotic behavior of the model in the sense of Marotto is proved. To verify the results obtained analytically, we perform numerical simulations which also explore further the richer dynamics of the model.


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