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Theory and Modern Applications

Table 1 Parameters used in the new model

From: Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory

Symbol

Definition

\(r_{i}\)

birth rate for prey population on patch i

\(e_{i}x_{i}\)

functional response of predators on patch i

\(\gamma _{i}\)

death rate for predator population on patch i

\(\frac{{\varepsilon _{i}}}{{e_{i}}}\)

conversion rate of prey on patch i

\(\frac{{r_{i}}}{{b_{i}}}\)

environmental capacity for prey population on patch i

\(\frac{{\gamma _{i}}}{{\delta _{i}}}\)

environmental capacity for predator population on patch i

\(k_{ij}^{xy}\)

dispersal rate of predators from patch j to patch i

\(k_{ij}^{yx}\)

dispersal rate of prey from patch j to patch i

\(s_{ij}x_{i} \)

functional response of predators that disperse from patch j to patch i

\(p_{ij}x_{j}\)

functional response of predators on patch i to prey that disperse from patch j to patch i

\(z_{ij} \)

conversion rate of prey that come from patch j and are preyed on by predators on patch i