Limit cycles in a Kolmogorov‐type model

Huang, Xuncheng

doi:10.1155/s0161171290000795

Cited by 13 publications

(17 citation statements)

References 7 publications

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“…Our aim is to generalize and improve some results obtained in Ref. [ 1 ]. Consider the following generalized Gause-type predator-prey system…”

Section: Dt = V(y)(~b(x) + 8(y))mentioning

confidence: 86%

“…[ 1 ], where the ecological meaning of this model was discussed. Some special cases of system (1) have been studied by many authors [2-s] . Our aim is to generalize and improve some results obtained in Ref.…”

Section: Dt = V(y)(~b(x) + 8(y))mentioning

confidence: 99%

“…The qualitative behavior of solutions of the Gause-type biomathematical model -~=~(x)(F(x)-~r(y)) ay (1) …”

Section: Introductionmentioning

confidence: 99%

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Limit cycles in a generalized Gause-type predator-prey system

Chen

Liu

2001

J Cent. South Univ. Technol.

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The qualitative behavior of solutions for a generalized Game-type predator-prey system was studied. A large number of biological and bioeconomic models are special cases of this system. The system was investigated in the region D = / (x, y) I x > O, y > 0 t because of the biological meaning of the system. The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system, which ensure that the system has at least one limit cycle. The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare-Bendixson are efficiently employed in the research. The main results and their corrst~luences presented not only generalize some known results,but also improve some corresponding results of other authors.

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“…Our aim is to generalize and improve some results obtained in Ref. [ 1 ]. Consider the following generalized Gause-type predator-prey system…”

Section: Dt = V(y)(~b(x) + 8(y))mentioning

confidence: 86%

Section: Dt = V(y)(~b(x) + 8(y))mentioning

confidence: 99%

See 1 more Smart Citation

Limit cycles in a generalized Gause-type predator-prey system

Chen

Liu

2001

J Cent. South Univ. Technol.

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“…When F (x, y) and G(x, y) are polynomials of degrees 2, limit cycles can occur and there is an extensive literature dealing with their existence, number and stability (see for instance May [13], Lloyd, Pearson,Saèz and Szántó [11,12], Huang [8], Huang, Wang, Cheng [9], Huang, Zhu [10], Boqian and Demeng [4], Cheng [5], and references therein), but to our knowledge, the exact analytic expressions of the limit cycles for a given kolmogorov system is still unknown except in simplest and specific cases.…”

Section: Introductionmentioning

confidence: 99%

Kolmogorov System with Explicit Hyperbolic Limit Cycle

Benyoucef¹,

Bendjeddou²,

Бенусеф³

et al. 2017

J. Sib. Fed. Univ., Math. phys.

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“…If F and G are linear (Lotka-VolterraGause model), then it is well known that there is at most one critical point in the interior of the realistic quadrant (x 0, y 0), and there are no limit cycles [10,14,16]. There are many natural phenomena which can be modeled by the Kolmogorov systems such as mathematical ecology and population dynamics [12,17,18] chemical reactions, plasma physics [13], hydrodynamics [5], etc.…”

Section: Introductionmentioning

confidence: 99%