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Hopf bifurcations in a three-species food chain system with multiple delays

100%
Xie X., Zhang W.
Open Mathematics
|
2017
|
tom 15
|
nr 1
508-519
EN
This paper is concerned with a three-species Lotka-Volterra food chain system with multiple delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the stability of the positive equilibrium and existence of Hopf bifurcations are investigated. Furthermore, the direction of bifurcations and the stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.
2
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Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls

76%
Lu L., Lian Y., Li C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
218-232
EN
This paper is concerned with a competition and cooperation model of two enterprises with multiple delays and feedback controls. With the aid of the difference inequality theory, we have obtained some sufficient conditions which guarantee the permanence of the model. Under a suitable condition, we prove that the system has global stable periodic solution. The paper ends with brief conclusions.
3
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The Poincaré-Bendixson Theorem: from Poincaré to the XXIst century

64%
Ciesielski K.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2110-2128
EN
The Poincaré-Bendixson Theorem and the development of the theory are presented - from the papers of Poincaré and Bendixson to modern results.
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