Nonlinear Resonance in Basin Portraits of Two Coupled Swings Under Periodic Forcing

DOI10.1142/S0218127498000930zbMath0963.70551OpenAlexW2040787011MaRDI QIDQ4936236

Ralph H. Abraham, Yoshinori Ueda, H. Bruce Stewart, Yoshisuke Ueda

Publication date: 25 January 2000

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127498000930

zbMATH Keywords

synchronizationtransmission networkperiodic attractordesynchronizationnonlinear resonancebus fluctuation frequencyelectric power supply networktwo-generator network

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Technical applications of optics and electromagnetic theory (78A55) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items

Invariant Sets in Quasiperiodically Forced Dynamical Systems ⋮ GLOBAL BASIN STRUCTURE OF ATTRACTION OF TWO DEGREES OF FREEDOM SWING EQUATION SYSTEM ⋮ Nonlinear dynamic singularity analysis of two interconnected synchronous generator system with \(1:3\) internal resonance and parametric principal resonance ⋮ TANGLED SEPARATRICES ON TWO DEGREES OF FREEDOM SWING EQUATION SYSTEM ⋮ OSCILLATIONAL RESPONSES AND BASIN STRUCTURE ON ONE-WELL QUINTIC POTENTIAL

Cites Work

• Catastrophes with indeterminate outcome
• Integrity measures quantifying the erosion of smooth and fractal basins of attraction
• Chaotic phenomena triggering the escape from a potential well
• Indeterminate jumps to resonance from a tangled saddle-node bifurcation