2017
DOI: 10.1515/math-2017-0023
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Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls

Abstract: 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.

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Cited by 6 publications
(3 citation statements)
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“…Overall, the feedback controls play a crucial role in achieving precise and stable operation in complex systems, enabling efficient and reliable performance in a wide range of applications. Recently, there have been a few studies [10][11][12] about the delayed non-autonomous competition and cooperation model of two enterprises that consider dynamic behaviors for feedback control cases. Based on the above analysis and as an extension of previously works [1][2][3][4][5][6]9], this paper will consider the following non-autonomous model with feedback controls and time delays:…”
Section: Introductionmentioning
confidence: 99%
“…Overall, the feedback controls play a crucial role in achieving precise and stable operation in complex systems, enabling efficient and reliable performance in a wide range of applications. Recently, there have been a few studies [10][11][12] about the delayed non-autonomous competition and cooperation model of two enterprises that consider dynamic behaviors for feedback control cases. Based on the above analysis and as an extension of previously works [1][2][3][4][5][6]9], this paper will consider the following non-autonomous model with feedback controls and time delays:…”
Section: Introductionmentioning
confidence: 99%
“…It has shown that time delay has an important impact on the steady-state equilibrium of the interactive relationship between enterprises. e latest research results of some delayed systems can be found in [7][8][9][10][11][12][13], which focus on multiple time delays and feedback control, fractional-order delay model, and discrete model with multiple delays.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, many scholars have proposed various types of models about enterprise clusters based on ecology theory and dynamic system theory, which sparked great interest in the study of dynamic properties of the enterprise clusters models [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. For example in [5], the authors considered the following autonomous model without time delay…”
Section: Introductionmentioning
confidence: 99%