  Motivated by the evolution of complex bird songs, an abstract imitation game
is proposed to study the increase of dynamical complexity: Artificial "birds"
display a "song" time series to each other, and those that imitate the other's
song better win the game. With the introduction of population dynamics
according to the score of the game and the mutation of parameters for the song
dynamics, the dynamics is found to evolve towards the borderline between chaos
and a periodic window, after punctuated equilibria. The importance of edge of
chaos with topological chaos for complexity is stressed.
