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1
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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

100%
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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Existence of solutions for delay evolution equations with nonlocal conditions

86%
Zhang X., Li Y.
Open Mathematics
|
2017
|
tom 15
|
nr 1
616-627
EN
In this paper, we are devoted to study the existence of mild solutions for delay evolution equations with nonlocal conditions. By using tools involving the Kuratowski measure of noncompactness and fixed point theory, we establish some existence results of mild solutions without the assumption of compactness on the associated semigroup. Our results improve and generalize some related conclusions on this issue. Moreover, we present an example to illustrate the application of the main results.
4
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Unbounded solutions of third order delayed differential equations with damping term

86%
Bartušek M., Cecchi M., Došlá Z., Marini M.
Open Mathematics
|
2011
|
tom 9
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nr 1
184-195
EN
Globally positive solutions for the third order differential equation with the damping term and delay, $$ x''' + q(t)x'(t) - r(t)f(x(\phi (t))) = 0, $$ are studied in the case where the corresponding second order differential equation $$ y'' + q(t)y = 0 $$ is oscillatory. Necessary and sufficient conditions for all nonoscillatory solutions of (*) to be unbounded are given. Furthermore, oscillation criteria ensuring that any solution is either oscillatory or unbounded together with its first and second derivatives are presented. The comparison of results with those in the case when (**) is nonoscillatory is given, as well.
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