Table 3 Analysis of equilibrium points by the eigenvalues of the Jacobian matrix J.

From: Analysis of long-term strategies of riparian countries in transboundary river basins

Condition

Equilibrium point

Sign of eigenvalues

Stability status

1

(0, 0, 0)

(?, ?, ?)

Uncertain stable point

2

(1, 0, 0)

(?, ?, ?)

Uncertain stable point

3

(0, 1, 0)

(?, ?, ?)

Uncertain stable point

4

(0, 0, 1)

(?, ?, ?)

Uncertain stable point

5

(1, 1, 0)

(?, ?, +)

Unstable point

6

(1, 0, 1)

(?, + , ?)

Unstable point

7

(0, 1, 1)

(?, ?, ?)

Uncertain stable point

8

(1, 1, 1)

(?, −, −)

Uncertain stable point

  1. “ + ” means positive sign of eigenvalue; “ − ” means negative sign of eigenvalue; “?” means uncertain sign of eigenvalue.