Figure 10: Travelling wave behaviour for Equation (21) with the strong Allee effect and positive-negative-positive F(C) (Case 6.3). | Scientific Reports

Figure 10: Travelling wave behaviour for Equation (21) with the strong Allee effect and positive-negative-positive F(C) (Case 6.3).

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

Figure 10

(a,d) Phase plane for the system (24 and 25) with the numerical solution of Equation (21) (cyan, solid), in (C, U) co-ordinates, superimposed. The dashed black lines denote a wall of singularities. Red circles correspond to equilibrium points and purple circles correspond to holes in the wall. (b,e) Numerical solution of Equation (21) calculated at (b) t = 200 and t = 400; (e) t = 500 and t = 1000. The grey lines indicate the initial condition and the arrows indicate the direction of increasing time. The insets correspond to the areas within the red dashed lines, and highlight the shocks. (c,f) The time evolution of L(t). All results are obtained with δx = 0.05, δt = 0.001, ε = 10−6, , (a–c) , , , , , v = 0.009; (d–f) , , , , , v = −0.028.

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