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Beyond fixed points: transient quasi-stable dynamics emerging from ghost channels and ghost cycles

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Koch,  Daniel       
Lise Meitner Group Cellular Computations and Learning, Max Planck Institute for Neurobiology of Behavior – caesar, Max Planck Society;

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Nandan,  Akhilesh P.       
Lise Meitner Group Cellular Computations and Learning, Max Planck Institute for Neurobiology of Behavior – caesar, Max Planck Society;

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Ramesan,  Gayathri       
Lise Meitner Group Cellular Computations and Learning, Max Planck Institute for Neurobiology of Behavior – caesar, Max Planck Society;
International Max Planck Research School (IMPRS) for Brain and Behavior, Max Planck Institute for Neurobiology of Behavior – caesar, Max Planck Society;

/persons/resource/persons118347

Koseska,  Aneta       
Lise Meitner Group Cellular Computations and Learning, Max Planck Institute for Neurobiology of Behavior – caesar, Max Planck Society;

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2309.17201.pdf
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Citation

Koch, D., Nandan, A. P., Ramesan, G., & Koseska, A. (2023). Beyond fixed points: transient quasi-stable dynamics emerging from ghost channels and ghost cycles. doi:10.48550/arXiv.2309.17201.


Cite as: https://hdl.handle.net/21.11116/0000-000D-D68F-1
Abstract
Dynamical description of natural systems has generally focused on fixed points, with saddles and saddle-based phase space objects such as heteroclinic channels and heteroclinic cycles being central concepts behind the emergence of quasi-stable dynamics or long transients. Reliable and robust quasi-stable dynamics observed for real, inherently noisy systems is, however, not met by saddle-based dynamics, as demonstrated here. Generalizing the notion of ghost states, we provide a complementary framework for emergence of sequential quasi-stable dynamics that does not rely on (un)stable fixed points, but rather on slow directed flows on ghost manifolds from which ghost channels and ghost cycles are generated. Moreover, we show that these novel phase space objects are an emergent property of a broad class of models, typically used for description of natural systems.