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Spatial dynamics in a predator-prey model with herd behavior
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10.1063/1.4812724
/content/aip/journal/chaos/23/3/10.1063/1.4812724
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/3/10.1063/1.4812724
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The Turing space (marked T) of model (5) with . Area T which is located above the positive equilibrium existence line (the black line ), and bounded by the Hopf bifurcation line (the blue line ) and the Turing bifurcation line (the red line ).

Image of FIG. 2.
FIG. 2.

The relation between (the real part of the eigenvalue λ) and with ,  = 0.8 and different . Curve (1): ; Curve (2): ; Curve (3): ; Curve (4): ; Curve (5): .

Image of FIG. 3.
FIG. 3.

Bifurcation diagram of model (5) with ,  = 0.8. : hexagonal patterns with : hexagonal patterns with ; : stripe patterns. Solid lines: stable states; dashed lines: unstable states. .

Image of FIG. 4.
FIG. 4.

The three categories of Turing patterns of the prey in model (5) with parameters ,  = 0.8. (a)  = 0.989; (b)  = 0.949; (c)  = 0.927. Moments: (a)  = 25 000; (b)  = 20 000; (c)  = 20 000.

Image of FIG. 5.
FIG. 5.

Snapshots of contour pictures of the time evolution of the prey at different instants with ,  = 0.8,  = 0.989. Moments: (a)  = 0; (b)  = 5000; (c)  = 6000; (d)  = 6500; (e)  = 7000; (f)  = 25 000.

Image of FIG. 6.
FIG. 6.

Snapshots of contour pictures of the time evolution of the prey at different instants with ,  = 0.8,  = 0.949. Moments: (a)  = 0; (b)  = 250; (c) = 1000; (d)  = 1500; (e)  = 2500; (f)  = 20 000.

Image of FIG. 7.
FIG. 7.

Snapshots of contour pictures of the time evolution of the prey at different instants with ,  = 0.8,  = 0.927. Moments: (a)  = 0; (b)  = 50; (c) = 500; (d)  = 2500; (e)  = 10000; (f)  = 20 000.

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/content/aip/journal/chaos/23/3/10.1063/1.4812724
2013-07-08
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spatial dynamics in a predator-prey model with herd behavior
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/3/10.1063/1.4812724
10.1063/1.4812724
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