  The paper presents a method by which the mean field dynamics of a population
of dynamical systems with parameter diversity and global coupling can be
described in terms of a few macroscopic degrees of freedom. The method applies
to populations of any size and functional form in the region of coherence. It
requires linear variation or a narrow distribution for the dispersed parameter.
Although being an approximation, the method allows us to quantitatively study
the collective regimes that arise as a result of diversity and coupling and to
interpret the transitions among these regimes as bifurcations of the effective
macroscopic degrees of freedom. To illustrate, the phenomenon of oscillator
death and the route to full locking are examined for chaotic oscillators with
time scale mismatch.
