Dynamical systems, attractors, and neural circuits
Abstract: Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic—they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions
- Standort
-
Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
-
Online-Ressource
- Ausgabe
-
Version 1
- Sprache
-
Englisch
- Anmerkungen
-
F1000Research. - 5 (2016) , 992, ISSN: 2046-1402
- Ereignis
-
Veröffentlichung
- (wo)
-
Freiburg
- (wer)
-
Universität
- (wann)
-
2020
- Urheber
- Beteiligte Personen und Organisationen
-
Data Analysis and Modeling of Dynamic Processes in the Life Science
- DOI
-
10.12688/f1000research.7698.1
- URN
-
urn:nbn:de:bsz:25-freidok-1531436
- Rechteinformation
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
-
25.03.2025, 13:43 MEZ
Datenpartner
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Miller, Paul
- Data Analysis and Modeling of Dynamic Processes in the Life Science
- Universität
Entstanden
- 2020
Ähnliche Objekte (12)
Koopmanism for Attractors in Dynamical Systems
Time series analysis and dynamical modeling in neural development
Functional interrogation of neural circuits with virally transmitted optogenetic tools
Infinite-dimensional dynamical systems, Volume 2.. Attractors and methods
Infinite-dimensional dynamical systems, Volume 1.. Attractors and inertial manifolds
Optimal dynamical control of many-body entanglement
AMULET 2.0 for verifying multiplier circuits
Estimating neural background input with controlled and fast perturbations: a bandwidth comparison between inhibitory opsins and neural circuits
The effect of Hebbian plasticity on the attractors of a dynamical system
Design and implementation of cause-based and consequence-based control circuits for active charge balancing in CMOS integrated neural stimulator
Quantifying agents’ causal responsibility in dynamical systems
Dynamical localization in more than one dimension
Koopmanism for Attractors in Dynamical Systems
Time series analysis and dynamical modeling in neural development
Functional interrogation of neural circuits with virally transmitted optogenetic tools
Infinite-dimensional dynamical systems, Volume 2.. Attractors and methods
Infinite-dimensional dynamical systems, Volume 1.. Attractors and inertial manifolds
Optimal dynamical control of many-body entanglement
AMULET 2.0 for verifying multiplier circuits
Estimating neural background input with controlled and fast perturbations: a bandwidth comparison between inhibitory opsins and neural circuits
The effect of Hebbian plasticity on the attractors of a dynamical system
Design and implementation of cause-based and consequence-based control circuits for active charge balancing in CMOS integrated neural stimulator
Quantifying agents’ causal responsibility in dynamical systems
Dynamical localization in more than one dimension
Koopmanism for Attractors in Dynamical Systems
Time series analysis and dynamical modeling in neural development
Functional interrogation of neural circuits with virally transmitted optogenetic tools
Infinite-dimensional dynamical systems, Volume 2.. Attractors and methods
Infinite-dimensional dynamical systems, Volume 1.. Attractors and inertial manifolds
Optimal dynamical control of many-body entanglement
AMULET 2.0 for verifying multiplier circuits
Estimating neural background input with controlled and fast perturbations: a bandwidth comparison between inhibitory opsins and neural circuits
The effect of Hebbian plasticity on the attractors of a dynamical system
Design and implementation of cause-based and consequence-based control circuits for active charge balancing in CMOS integrated neural stimulator
Quantifying agents’ causal responsibility in dynamical systems