Evolution of attractors in quasiperiodically forced systems: From quasiperiodic to strange nonchaotic to chaotic

Journal Article · Wed Mar 01 00:00:00 EST 1989 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.39.2593· OSTI ID:6339207

Ding, M; Grebogi, C; Ott, E

As a model displaying typical features of two-frequency quasiperiodically forced systems, we discuss the circle map with quasiperiodic coupling. We present numerical and analytical evidence for the existence of strange nonchaotic attractors, and we use examples to illustrate various types of dynamical behavior that can arise in typical quasiperiodically forced systems. We investigate the behavior of the system in the two-dimensional parameter plane of nonlinearity strength versus one of the driving frequencies. We find that the set in this parameter plane for which the system exhibits strange nonchaotic attractors has Cantor-like structure and is enclosed between two critical curves. One of these curves marks the transition from three-frequency quasiperiodic attractors to strange nonchaotic attractors; the other marks the transition from strange nonchaotic attractors to chaotic attractors. This suggests a possible route to chaos in two-frequency quasiperiodically forced systems: (three-frequency quasiperiodicity)..-->..(strange nonchaotic behavior)..-->..(chaos).

• Research Organization: Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742
• OSTI ID: 6339207
• Journal Information: Phys. Rev. A; (United States), Vol. 39:5
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DYNAMICS
QUASILINEAR PROBLEMS
EQUATIONS OF MOTION
FREQUENCY ANALYSIS
HARMONICS
MAPPING
OSCILLATORS
TRAJECTORIES
DIFFERENTIAL EQUATIONS
ELECTRONIC EQUIPMENT
EQUATIONS
EQUIPMENT
MECHANICS
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics