What is an isocline?

Answer 1

http://en.wikipedia.org/wiki/Isocline An Isocline is a series of lines with the same slope. The word comes from the Greek words Isos (Ίδιος) meaning "same" and Klini (κλίση) meaning "slope." It is often used as a graphical method of solving ordinary differential equations. In an equation of the form y' = f(x), the isoclines are given putting f(x) equal to a constant. This gives a series of lines (for different constants) along which the solution curves have the same gradient. By calculating this gradient for each isocline, the slope field can be visualised; making it relatively easy to sketch approximate solution curves; as in fig. 1. In population dynamics refers to the set of population sizes at which the rate of change, or partial derivative, for one population in a pair of interacting populations is zero.

Answer 2

An isocline is a curve on a graph where the slope of a function is constant. Isoclines are used to identify equilibrium points in systems of differential equations, where the variables do not change. They help determine the direction of movement of solutions in phase space.