Permanence for Lotka–Volterra systems with multiple delays

Lu, Guichen; Lu, Zhengyi; Enatsu, Yoichi

doi:10.1016/j.nonrwa.2011.03.004

Cited by 8 publications

(8 citation statements)

References 10 publications

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“…In addition, numerical simulation results shows the feasibility of our results. Moreover, the models and results present in this paper can been seen as the improvement and extension of the models and results obtained in [2,4,7,9,10,12].…”

Section: Resultsmentioning

confidence: 54%

Dynamic analysis of competing predator-prey systems with pure delays

2020

J. Nonlinear Funct. Anal.

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Two classes of nonautonomous three-species Lotka-Volterra type one predator-two competitive prey systems with pure discrete time delays are investigated. Some new sufficient conditions on the boundedness, the permanence, the extinction and the global attractivity of the systems are established by using the comparison method and the construction of suitable Lyapunov functional. Finally, the theoretical results are illustrated by one example with numerical simulations.

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Section: Resultsmentioning

confidence: 54%

Dynamic analysis of competing predator-prey systems with pure delays

2020

J. Nonlinear Funct. Anal.

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“…Many scholars have studied cooperative systems and obtained good results. For example, authors that considered the problem of determining the permanence or persistence of non-autonomous multi-species L-V systems with and without delays managed to obtain some criteria for the permanence or persistence of the systems they studied [7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Dynamics in an n-Species Lotka–Volterra Cooperative System with Delays

Zhao

Halik

Muhammadhaji

2023

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We studied a class of generalized n-species non-autonomous cooperative Lotka–Volterra (L-V) systems with time delays. We obtained new criteria on the dynamic properties of the systems. First, we obtained the boundedness and permanence of the system using the inequality analysis technique and comparison method. Then, the existence of positive periodic solutions was investigated using the coincidence degree theory. The global attractivity of the system was obtained by constructing suitable Lyapunov functionals and utilizing Barbalat’s lemma. The existence and global attractivity of the periodic solutions were also obtained. Finally, we conducted two numerical simulations to validate the feasibility and practicability of our results.

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“…where A i is the ith row of the N × N matrix A, Jansen [11] (see also [7,Ch.13]) proved that (1) is permanent if there is a vector q ∈ intR N + such that the inequality q T (r + Ax) > 0 holds for every fixed pointx ∈ ∂R N + . Examples of permanence for special delayed Kolmogorov systems are given by Chen, Lu and Wang [5], Hou [8]- [10], Li and Teng [13], Liu and Chen [14], Lu, Lu and Enatsu [15], Mukherjee [16], Teng [19], and the references therein. In particular, for autonomous Lotka-Volterra differential systems with multiple delays, sufficient conditions for permanence, which are easily checkable inequalities involving the constant coefficients of the system, were obtained in [15].…”

Section: Introductionmentioning

confidence: 99%

“…[5], Hou [8][9][10], Li and Teng [13], Liu and Chen [14], Lu et al . [15], Mukherjee [17], Teng [19], and the references therein. In particular, for autonomous Lotka-Volterra differential systems with multiple delays, sufficient conditions for perma-Z.…”

Section: Introductionmentioning

confidence: 99%

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Permanence criteria for Kolmogorov systems with delays

Hou¹

2014

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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In this paper, a class of Kolmogorov systems with delays are studied. Sufficient conditions are provided for a system to have a compact uniform attractor. Then Jansen's result for autonomous replicator and Lotka-Volterra systems has been extended to delayed non-autonomous Kolmogorov systems with periodic or autonomous Lotka-Volterra subsystems. Thus, simple algebraic conditions are obtained for partial permanence and permanence. An outstanding feature of all these results is that the conditions are independent of the size and distribution of the delays.

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Permanence for Lotka–Volterra systems with multiple delays

Cited by 8 publications

References 10 publications

Dynamic analysis of competing predator-prey systems with pure delays

Dynamic analysis of competing predator-prey systems with pure delays

Dynamics in an n-Species Lotka–Volterra Cooperative System with Delays

Permanence criteria for Kolmogorov systems with delays

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