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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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Global bifurcation of homoclinic trajectories of discrete dynamical systems

76%
Pejsachowicz J., Skiba R.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2088-2109
EN
We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving topological properties of the asymptotic stable bundles.
3
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Some global results for nonlinear fourth order eigenvalue problems

52%
Aliyev Z.
Open Mathematics
|
2014
|
tom 12
|
nr 12
1811-1828
EN
In this paper, we consider the nonlinear fourth order eigenvalue problem. We show the existence of family of unbounded continua of nontrivial solutions bifurcating from the line of trivial solutions. These global continua have properties similar to those found in Rabinowitz and Berestycki well-known global bifurcation theorems.
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