Global stability properties of equilibria, periodic, and chaotic solutions

DOI10.1016/0307-904X(95)00168-JzbMath0857.34054MaRDI QIDQ1922274

Mohamed S. Soliman

Publication date: 15 September 1996

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

zbMATH Keywords

stabilitynonlinear dynamical systemsbasins of attractionfractal basin boundariesstability of higher order periodic and chaotic solutionstransitions across basin boundaries

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability of solutions to ordinary differential equations (34D20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Complex behavior and chaotic systems of ordinary differential equations (34C28) Attractors of solutions to ordinary differential equations (34D45) Stability theory for smooth dynamical systems (37C75)

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Cites Work

• Stability by Liapunov's direct method. With applications
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Fractal basin boundaries
• Integrity measures quantifying the erosion of smooth and fractal basins of attraction
• BASIN ORGANIZATION PRIOR TO A TANGLED SADDLE-NODE BIFURCATION
• Jumps to Resonance: Long Chaotic Transients, Unpredictable Outcome, and the Probability of Restabilization
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