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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. \(\frac{\alpha}{1 - \alpha} \sqrt{\frac {D_{0}}{D}}\) [8, 16]
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. \(\frac{\alpha}{1 - \alpha} \frac {D_{0}}{D}\) [8, 16]
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. \(\frac{\alpha}{1 - \alpha}\) [17, 18]