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Theory and Modern Applications

Figure 3 | Advances in Difference Equations

Figure 3

From: Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure

Figure 3

Self-organziation and nonlinear properties of a spiral-spot pattern. (a)–(d) Evolution of the prey pattern at transient times \(t =10\), \(t =100\), \(t =1000\), and \(t =10{,}000\), respectively; (e)–(g) wave diagrams and phase portrait of the prey and the predator in a random site of the predator and prey patterns; (h) maximum Lyapunov exponent diagram corresponding to the prey pattern. The parameter values are given as \(a = 1.1\), \(e_{1} = 0.3\), \(e_{2} = 0.2\), \(b = 0.3739\), \(\tau = 2.828\), \(\delta = 3.2\), \(h = 8\), \(n= 100\)

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