| Citation: |
Jianzhi Cao, Li Ma, Pengmiao Hao. BIFURCATION ANALYSIS IN A MODIFIED LESLIE-GOWER PREDATOR-PREY MODEL WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 3026-3053. doi: 10.11948/20230183
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BIFURCATION ANALYSIS IN A MODIFIED LESLIE-GOWER PREDATOR-PREY MODEL WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE
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Abstract
This paper investigates the dynamics of a modified Leslie-Gower predator-prey model with Bedington-DeAngelis functional response. Some properties are explored, including positivity, dissipativity, permanence, and stability. In addition, the transcritical bifurcation and Hopf bifurcation taking $ d $ as the bifurcation parameter and Bogdanov-Takens bifurcation taking $ d $ and $ n $ as bifurcation parameters are studied. The theoretical results of this paper are verified by numerical simulation. The results show that the system has rich dynamical behaviors.
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References
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Jianzhi Cao, Li Ma, Pengmiao Hao. BIFURCATION ANALYSIS IN A MODIFIED LESLIE-GOWER PREDATOR-PREY MODEL WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 3026-3053. doi: 10.11948/20230183
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Figure 1.
Number of positive equilibrium under parameter conditions.
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Figure 2.
(a) the transcritical bifurcation diagram around
$ A_{3}(0, \frac{mp}{n}) $ $ e=0.07, m=0.2, n=0.6, p=0.4 $ $ d=0.05 $ $ d=0.15 $ -
Figure 3.
(a) Hopf bifurcation around
$ E^*(0.10978, 0.6797) $ $ e=0.2, m=0.02, n=0.015, p=0.4 $ $ d=0.53 $ $ d=0.51 $ -
Figure 4.
Phase diagram near Bogdanov-Takens bifurcation point when
$ d_{BT}=0.08975, e=0.12, m=0.2, n_{BT}=0.3899, p=0.3 $ $ (\epsilon_{1}, \epsilon_{2})=(-0.00775, 0.0001) $ $ (\epsilon_{1}, \epsilon_{2})=(0.00002, 0.0112) $ $ (\epsilon_{1}, \epsilon_{2})=(0.0008, 0.0112) $ $ (\epsilon_{1}, \epsilon_{2})=(0.00325, 0.0112) $ $ (\epsilon_{1}, \epsilon_{2})=(0.00525, 0.0112) $