Table 1 Listing of interface scenarios with descriptions and selected references from [12]
From: An exact bifurcation diagram for a reaction–diffusion equation arising in population dynamics
Scenario name | Scenario description | κ | References |
|---|---|---|---|
Continuous density | Organisms move between the patch and the matrix with equal probability. Step sizes and movement probabilities are equal in the patch and the matrix. | 1 | [15] |
Type I Discontinuous density (DD) | Organisms modify their movement behavior at the patch/matrix interface and would have a probability α of remaining in or leaving Ω different from 50%. Step sizes differ between the patch and the matrix, whereas movement probabilities are equal. | \(\frac{\alpha}{1 - \alpha} \sqrt{\frac {D_{0}}{D}}\) | |
Type II Discontinuous density (DD) | Organisms modify their movement behavior at the patch/matrix interface and would have a probability α of remaining in or leaving Ω different from 50%. Step sizes are equal between the patch and the matrix but movement probabilities are different. | \(\frac{\alpha}{1 - \alpha} \frac {D_{0}}{D}\) | |
Type III Discontinuous density (DD) | Organisms remain in Ω with probability α different from 50%. Movement probabilities and step sizes are the same between the patch and the matrix. | \(\frac{\alpha}{1 - \alpha}\) |