| Citation: |
Sobirjon Shoyimardonov. NEIMARK-SACKER BIFURCATION AND STABILITY ANALYSIS IN A DISCRETE PHYTOPLANKTON-ZOOPLANKTON SYSTEM WITH HOLLING TYPE Ⅱ FUNCTIONAL RESPONSE[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2048-2064. doi: 10.11948/20220345
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NEIMARK-SACKER BIFURCATION AND STABILITY ANALYSIS IN A DISCRETE PHYTOPLANKTON-ZOOPLANKTON SYSTEM WITH HOLLING TYPE Ⅱ FUNCTIONAL RESPONSE
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Abstract
In this paper, we study discrete-time model of phytoplankton-zooplankton with Holling type Ⅱ predator functional response. It is shown that Neimark-Sacker bifurcation occurs at the one of positive fixed points for certain parameter chosen as a bifurcation parameter. The existence and local stability of the positive fixed points of the model are proved. By considering theoretical results in the concrete example, it was obtained interesting dynamics of this system, which is not investigated in its corresponding continuous system.
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References
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Sobirjon Shoyimardonov. NEIMARK-SACKER BIFURCATION AND STABILITY ANALYSIS IN A DISCRETE PHYTOPLANKTON-ZOOPLANKTON SYSTEM WITH HOLLING TYPE Ⅱ FUNCTIONAL RESPONSE[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2048-2064. doi: 10.11948/20220345
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Figure 1.
Phase portraits for the system (1.4) with
$ c=1, \beta=4, r=10/9, \theta_0=4/9\approx0.4444..., (u^0, v^0)=(0.6, 0.75). $ -
Figure 2.
Phase portraits for the system (1.4) with
$ c=1, \beta=4, r=10/9, \theta_0=4/9\approx0.4444.... $