| Citation: |
Rui Ma, Yuzhen Bai, Fei Wang. DYNAMICAL BEHAVIOR ANALYSIS OF A TWO-DIMENSIONAL DISCRETE PREDATOR-PREY MODEL WITH PREY REFUGE AND FEAR FACTOR[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1683-1697. doi: 10.11948/20190426
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DYNAMICAL BEHAVIOR ANALYSIS OF A TWO-DIMENSIONAL DISCRETE PREDATOR-PREY MODEL WITH PREY REFUGE AND FEAR FACTOR
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Abstract
This paper investigates the dynamics of an improved discrete Leslie-Gower predator-prey model with prey refuge and fear factor. First, a discrete Leslie-Gower predator-prey model with prey refuge and fear factor has been introduced. Then, the existence and stability of fixed points of the model are analyzed. Next, the bifurcation behaviors are discussed, both flip bifurcation and Neimark-Sacker bifurcation have been studied. Finally, some simulations are given to show the effectiveness of the theoretical results. -
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References
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Rui Ma, Yuzhen Bai, Fei Wang. DYNAMICAL BEHAVIOR ANALYSIS OF A TWO-DIMENSIONAL DISCRETE PREDATOR-PREY MODEL WITH PREY REFUGE AND FEAR FACTOR[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1683-1697. doi: 10.11948/20190426
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Figure 1. Bifurcation for map (1.4) at
$ E_{3} $ with initial values (3.4, 2.1). -
Figure 2. Phase portraits corresponding to Fig. 1, (a)
$ k $ = 0.63; (b)$ k $ = 0.64; (c)$ k $ = 0.65; (d)$ k $ = 0.66. -
Figure 3. The time responses for the state
$ x(t) $ and$ y(t) $ corresponding to Fig. 1, (a)$ k $ = 0.63; (b)$ k $ = 0.64; (c)$ k $ = 0.65; (d)$ k $ = 0.66. -
Figure 4. The time responses for the state
$ x(t) $ and$ y(t) $ , (a)$ k $ = 1.43; (b)$ k $ = 1.43; (c)$ k $ = 1.46; (d)$ k $ = 1.46. -
Figure 5. Phase portraits corresponding to Fig. 4, (a)
$ k $ = 1.43(a period-17 orbit); (b)$ k $ = 1.46.