Permanence in a Discrete Mutualism Model with Infinite Deviating Arguments and Feedback Controls

Xu, Changjin; Wu, Yusen

doi:10.1155/2013/397382

Cited by 3 publications

(1 citation statement)

References 35 publications

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“…Chen [11] argued that the general nonautonomous nonperiodic system is more appropriate, and he showed that the system (3) is permanent. For more work about cooperative system, we can refer to [12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Global Stability of a Discrete Mutualism Model

Yang

Xie

Chen

2014

Abstract and Applied Analysis

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A discrete mutualism model is studied in this paper. By using the linear approximation method, the local stability of the interior equilibrium of the system is investigated. By using the iterative method and the comparison principle of difference equations, sufficient conditions which ensure the global asymptotical stability of the interior equilibrium of the system are obtained. The conditions which ensure the local stability of the positive equilibrium is enough to ensure the global attractivity are proved.

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Section: Introductionmentioning

confidence: 99%

Global Stability of a Discrete Mutualism Model

Yang

Xie

Chen

2014

Abstract and Applied Analysis

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Dynamic behaviors of a non-selective harvesting May cooperative system incorporating partial closure for the populations

2018

cmbn

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Extremal values of VDB topological indices over F-benzenoids with equal number of edges

Rada

2023

MBE

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<abstract>The utilization of molecular structure topological indices is currently a standing operating procedure in the structure-property relations research, especially in QSPR/QSAR study. In the past several year, generous molecular topological indices related to some chemical and physical properties of chemical compounds were put forward. Among these topological indices, the VDB topological indices rely only on the vertex degree of chemical molecular graphs. The VDB topological index of an $ n $-order graph $ G $ is defined as <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ TI(G) = \sum\limits_{1\leq i\leq j\leq n-1}m_{ij}\psi_{ij}, $\end{document} </tex-math></disp-formula> where $ \{\psi_{ij}\} $ is a set of real numbers, $ m_{ij} $ is the quantity of edges linking an $ i $-vertex and another $ j $-vertex. Numerous famous topological indices are special circumstance of this expression. f-benzenoids are a kind of polycyclic aromatic hydrocarbons, present in large amounts in coal tar. Studying the properties of f-benzenoids via topological indices is a worthy task. In this work the extremum $ TI $ of f-benzenoids with given number of edges were determined. The main idea is to construct f-benzenoids with maximal number of inlets and simultaneously minimal number of hexagons in $ \Gamma_{m} $, where $ \Gamma_{m} $ is the collection of f-benzenoids with exactly $ m $ $ (m\geq19) $ edges. As an application of this result, we give a unified approach of VDB topological indices to predict distinct chemical and physical properties such as the boiling point, $ \pi $-electrom energy, molecular weight and vapour pressure etc. of f-benzenoids with fixed number of edges.</abstract>

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Permanence in a Discrete Mutualism Model with Infinite Deviating Arguments and Feedback Controls

Abstract: We propose and deal with a discrete mutualism model with infinite deviating arguments and feedback controls. Sufficient conditions which guarantee the permanence of the system are obtained by using the difference inequality theory. The paper ends with brief conclusions.

Cited by 3 publications

References 35 publications

Global Stability of a Discrete Mutualism Model

Global Stability of a Discrete Mutualism Model

Dynamic behaviors of a non-selective harvesting May cooperative system incorporating partial closure for the populations

Extremal values of VDB topological indices over F-benzenoids with equal number of edges

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