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1
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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.
2
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Dynamical behavior for a stochastic two-species competitive model

100%
Xu C., Liao M.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1258-1266
EN
This paper deals with a stochastic two-species competitive model. Some very verifiable criteria on the global stability of the positive equilibrium of the deterministic system are established. An example with its computer simulations is given to illustrate our main theoretical findings.
3
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Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances

84%
Chen F., Chen X., Huang S.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1157-1173
EN
A two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]. Numeric simulations are carried out to show the feasibility of our results.
4
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Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population

84%
Amar A.
Open Mathematics
|
2011
|
tom 9
|
nr 4
851-865
EN
Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary value problem arising in the theory of growing cell population in L 1-setting. Besides, a topological structure of the set of solutions is provided.
5
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The five-variable Volterra system

84%
Zieliński J.
Open Mathematics
|
2011
|
tom 9
|
nr 4
888-896
EN
We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.
6
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Rings of constants of four-variable Lotka-Volterra systems

84%
Zieliński J.
Open Mathematics
|
2013
|
tom 11
|
nr 11
1923-1931
EN
Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameters C 1, C 2, C 3, C 4 ∈ k, where k is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations.
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