Figure 3: Travelling wave behaviour for Equation (7) with positive-negative-positive F(C) (Case 2.3). | Scientific Reports

Figure 3: Travelling wave behaviour for Equation (7) with positive-negative-positive F(C) (Case 2.3).

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

Figure 3

(a,d) Phase plane for the system (9 and 10) with the numerical solution of Equation (7), in (C, U) co-ordinates, superimposed. The grey region corresponds to values of C where F(C) < 0. 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 (7) at t = 100 and t = 200. The grey lines indicate the initial condition and the arrows indicate the direction of increasing time. (c,f) The time evolution of the position of the leading edge of the travelling wave solution, L(t). All results are obtained using , δx = 0.01, , and (a–c) , , , v = 0.864; (d–f) , , , v = 0.448.

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