Abstract
High-dimensional chaos has been an area of growing recent investigation. The 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 paper, 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 subsystem becomes chaotic, leading to additional positive Lyapunov exponents for the whole system. A characteristic feature of this route is that the additional 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.
Original language | English |
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Pages (from-to) | 1471-1483 |
Number of pages | 13 |
Journal | International Journal of Bifurcation and Chaos |
Volume | 10 |
Issue number | 6 |
Publication status | Published - Jun 2000 |
Keywords
- DYNAMICAL-SYSTEMS
- PERIODIC-ORBITS
- RING CAVITY
- ATTRACTORS
- TRANSITION
- HYPERCHAOS
- OSCILLATORS
- SYNCHRONIZATION
- INSTABILITY
- COMPLEXITY