Bifurcation to high-dimensional chaos

High-dimensional chaos has been an area of growing recent investigation. Th e questions of how dynamical systems become high-dimensionally chaotic with multiple positive Lyapunov exponents, and what the characteristic features associated with the transition are, remain less investigated. In this pape r, we present one possible route to high-dimensional chaos. By this route, a subsystem becomes chaotic with one positive Lyapunov exponent via one of the known routes to low-dimensional. chaos, after which the complementary s ubsystem becomes chaotic, leading to additional positive Lyapunov exponents for the whole system. A characteristic feature of this route is that the a dditional Lyapunov exponents pass through zero smoothly. As a consequence, the fractal dimension of the chaotic attractor changes continuously through the transition, in contrast to the transition to low-dimensional chaos at which the fractal dimension changes abruptly. We present a heuristic theory and numerical examples to illustrate this route to high-dimensional chaos.