Isoclines and Global Stability
127
5.3 Isoclines and Global Stability
In a general. two-dimensional dynamic system described by a pair of
differential equations Xl = 11 (Xl' X 2 ) and x 2 = 12 (X" x 2 ). it is usually quite easy
to study the global stability properties by graphical analysis of the so-called
isocline curves; '" (x" x2) = 0 and 12 (Xl' X2) = 0 (e.g .• Rosenzweig and
Fig. 5.2. Location of the plane defined by Eq. (5.7) in the (P, C, Z) space, showing intersections
with the isocline surfaces for the algae (C) and the grazers (Z). Open circles mark locally
unstable stationary points; filled circles mark locally stable stationary points
127
5.3 Isoclines and Global Stability
In a general. two-dimensional dynamic system described by a pair of
differential equations Xl = 11 (Xl' X 2 ) and x 2 = 12 (X" x 2 ). it is usually quite easy
to study the global stability properties by graphical analysis of the so-called
isocline curves; '" (x" x2) = 0 and 12 (Xl' X2) = 0 (e.g .• Rosenzweig and
Fig. 5.2. Location of the plane defined by Eq. (5.7) in the (P, C, Z) space, showing intersections
with the isocline surfaces for the algae (C) and the grazers (Z). Open circles mark locally
unstable stationary points; filled circles mark locally stable stationary points