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Advances in Continuous and Discrete Models

Theory and Modern Applications

Figure 1 | Advances in Difference Equations

Figure 1

From: Stability analysis and traveling wave solution of a reaction–diffusion model for fish population incorporating time-dependent recruitment intensity

Figure 1

Phase portrait. (a) Plot of the phase portrait of the model system (7)–(8) showing solution trajectories in the vicinity of the two steady states, one of which is a saddle point and the other a stable focus as predicted by Theorem 1. Here, \(S_{1}\) is the steady state (\(u_{1},0\)) and \(S_{2}\) is (\(u_{2},0\)). (b) Plot of fish population density u as a function of traveling wave coordinate for t between 0 and 9. Here, \(a = \frac{1}{2}\), \(b = 2\), \(c = 4\), \(\rho = \frac{1}{2}\), \(k = \frac{1}{2}\), \(m = 1\), \(\tau = 2\), \(v = \frac{1}{2}\), and \(w = 1\)

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