Abstract
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.
Original language | English |
---|---|
Pages (from-to) | R3799-R3802 |
Number of pages | 4 |
Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
Volume | 59 |
Issue number | 4 |
Publication status | Published - Apr 1999 |
Keywords
- PERIODIC-ORBITS
- DYNAMIC-SYSTEMS
- TRANSITION
- ATTRACTORS
- TURBULENCE
- HYPERCHAOS
- EQUATIONS
- CRISES
- MAPS