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Everything about Attractor
Limiting set in dynamical systems
In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: AttractorA 5-minute orientation
- Skim a recent paper: Attractor and integrator networks in the brainInfluential work since 2022
- Pick up a classic book: Global attractors in abstract parabolic problemsThe most-reprinted book on the subject
- Read the landmark paper: YET ANOTHER CHAOTIC ATTRACTORCited 2,550 times
- Go sideways: HĂ©non mapA closely related topic
- Go sideways: Poincaré–Bendixson theoremA closely related topic
đź“– Definitions
Noun Something which attracts.
Noun A set of points or states to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed.
🏆 Landmark papers (most cited)
YET ANOTHER CHAOTIC ATTRACTOR
A two-dimensional mapping with a strange attractor
A NEW CHAOTIC ATTRACTOR COINED
Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors
Path Integration and Cognitive Mapping in a Continuous Attractor Neural Network Model
Accurate Path Integration in Continuous Attractor Network Models of Grid Cells
HIDDEN ATTRACTORS IN DYNAMICAL SYSTEMS. FROM HIDDEN OSCILLATIONS IN HILBERT–KOLMOGOROV, AIZERMAN, AND KALMAN PROBLEMS TO HIDDEN CHAOTIC ATTRACTOR IN CHUA CIRCUITS
On the concept of attractor
🆕 Influential since 2022
Attractor and integrator networks in the brain
An approximate line attractor in the hypothalamus encodes an aggressive state
Memristor Synapse-Driven Simplified Hopfield Neural Network: Hidden Dynamics, Attractor Control, and Circuit Implementation
Memristive Tabu Learning Neuron Generated Multi-Wing Attractor With FPGA Implementation and Application in Encryption
Causal evidence of a line attractor encoding an affective state
đź“š Books worth reading
Global attractors in abstract parabolic problemsJan W. Cholewa · 2000
Global attractors of non-autonomous dissipative dynamical systemsDavid N. Cheban · 2004
The creation of strange non-chaotic attractors in non-smooth saddle-node bifurcationsTobias H. Jäger · 2009
The theory of chaotic attractorsBrian R. Hunt · 2004- 📕Multi-pulse evolution and space-time chaos in dissipative systemsSergey Zelik · 2009
Strange nonchaotic attractorsUlrike Feudel · 2006- 📕Global Attractors of Non-Autonomous Dynamical and Control SystemsDavid N. Cheban · 2014
Infinite-dimensional Dynamical SystemsBoling Guo, Liming Ling · 2018
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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