Route to high-dimensional chaos

We present a route to high-dimensional chaos, that is, chaos with more than one positive Lyapunov exponent. In this route, as a system parameter changes, a subsystem becomes chaotic through, say, a cascade of period-doubling bifurcations, after which the complementary subsystem becomes chaotic, leading to an additional positive Lyapunov exponent for the whole system. A characteristic feature of this route, as suggested by numerical evidence, is that the second largest Lyapunov exponent passes through zero continuously. Three examples are presented: a discrete-time map, a continuous-time flow, and a population model for species dispersal in evolutionary ecology.