Chaos: An Introduction to Dynamical Systems
Abstract
One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.
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The equilibrium point x=x(Q) in Fig. 20 is asymptotically stable because the solution x(t) starting from any initial state x(0) ≠ x(Q) must tend to x(Q) as t→∞.
“The equilibrium point x = x ( Q ) in Fig. 20 is said to be asymptotically stable 10 in the Theory of Nonlinear Dynamics [27] because the solution x ( t ) starting from any initial state x (0) ≠ x(Q ) must tend to the equilibrium point x = x ( Q ) as t → ∞ .”
From Everything You Wish to Know About Memristors But Are Afraid to Ask (2015) · cites this paper as [27]
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- Authors
- Alligood, K. T., Sauer, T. D., Yorke, J. A., & Crawford, J. D.
- Affiliations
- University of Pittsburgh (US)
- Venue
- Physics Today
- Publisher
- AIP Publishing
- Published
- 1997-11-01
- Volume
- 50
- Issue
- 11
- Pages
- 67-68
- ISSN
- 0031-9228 (ISSN-L)
- 1945-0699
- OpenAlex
- W2015451024
- Cited by
- 1,469
- References
- 0
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 6 · 2023: 3 · 2022: 8 · 2021: 35 · 2020: 40 · 2019: 48 · 2018: 68 · 2017: 52 · 2016: 58 · 2015: 86 · 2014: 73 · 2013: 97 · 2012: 102
- Type
- book review
- Language
- en
- Open access
- closed
- Locations
- Physics Today (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Keywords
- chaos, dynamical systems, one-dimensional maps, two-dimensional maps, fractals, chaotic attractors, differential equations, periodic orbits, limit sets, stable manifolds, crisis, bifurcation, cascades
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