Figure 8: Travelling wave behaviour for Equation (21) with the strong Allee effect and extinction-degenerate non-negative F(C) (Case 6.2). | Scientific Reports

Figure 8: Travelling wave behaviour for Equation (21) with the strong Allee effect and extinction-degenerate non-negative F(C) (Case 6.2).

From: Co-operation, Competition and Crowding: A Discrete Framework Linking Allee Kinetics, Nonlinear Diffusion, Shocks and Sharp-Fronted Travelling Waves

Figure 8

(a,d) Phase plane for the system (24 and 25) with the numerical solution of Equations (21) (cyan, solid) and (23) (orange, dashed), in (C, U) co-ordinates, superimposed. Red circles correspond to equilibrium points. (b,e) Numerical solution of Equation (21) calculated at (b) t = 50 and t = 100; (e) t = 400 and t = 800. The grey lines indicate the initial condition and the arrows indicate the direction of increasing time. (c,f) The time evolution of L(t). All results are obtained with δx = 0.01, δt = 0.005, ε = 10−6, , , , (a–c) , , , v = 0.199; (d–f) , , , .

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