Temat: predator-prey model - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays
Autorzy:: Xu, C.
Liao, M.
He, X.
Powiązania:: https://bibliotekanauki.pl/articles/907822.pdf
Data publikacji:: 2011
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: opóźnienie
stabilność
bifurkacja Hopfa
predator-prey model
delay
stability
Hopf bifurcation
Opis:: In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also included.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2011, 21, 1; 97-107
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Bifurcation and control for a discrete-time prey–predator model with Holling-IV functional response
Autorzy:: Chen, Q.
Teng, Z.
Hu, Z.
Powiązania:: https://bibliotekanauki.pl/articles/907649.pdf
Data publikacji:: 2013
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: discrete prey predator model
flip bifurcation
Hopf bifurcation
saddle node bifurcation
OGY chaotic control
bifurkacja Hopfa
sterowanie chaosem
Opis:: The dynamics of a discrete-time predator–prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations in period-2, 4, 8, 16, quasi-periodic orbits, an attracting invariant circle, an inverse period-doubling bifurcation from the period-32 orbit leading to chaos and a boundary crisis, a sudden onset of chaos and a sudden disappearance of the chaotic dynamics, attracting chaotic sets and non-attracting sets. We also observe that when the prey is in chaotic dynamics the predator can tend to extinction or to a stable equilibrium. Specifically, we stabilize the chaotic orbits at an unstable fixed point by using OGY chaotic control.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2013, 23, 2; 247-261
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
Dostawca treści:: Biblioteka Nauki

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