Dynamical systems in neuroscience: the geometry of excitability and bursting
In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overvie...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, Mass. [u.a.]
MIT Press
2010
|
| Ausgabe: | 1. MIT Press paperback ed. |
| Schriftenreihe: | Computational neuroscience
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum--or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. |
| Beschreibung: | XVI, 441 S. Ill., graph. Darst. |
| ISBN: | 0262514206 9780262514200 9780262090438 |
Internformat
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| 100 | 1 | |a Ižikevič, Eugene M. |d 1967- |e Verfasser |0 (DE-588)137452446 |4 aut | |
| 245 | 1 | 0 | |a Dynamical systems in neuroscience |b the geometry of excitability and bursting |c Eugene M. Izhikevich |
| 250 | |a 1. MIT Press paperback ed. | ||
| 264 | 1 | |a Cambridge, Mass. [u.a.] |b MIT Press |c 2010 | |
| 300 | |a XVI, 441 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Computational neuroscience | |
| 520 | 3 | |a In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum--or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Models, Neurological | |
| 650 | 4 | |a Nerve Net |x physiology | |
| 650 | 4 | |a Neurology | |
| 650 | 4 | |a Neurons | |
| 650 | 4 | |a Neurons |x physiology | |
| 650 | 4 | |a Neurosciences | |
| 650 | 4 | |a Nonlinear Dynamics | |
| 650 | 0 | 7 | |a Neurowissenschaften |0 (DE-588)7555119-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Neurowissenschaften |0 (DE-588)7555119-6 |D s |
| 689 | 0 | 1 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | |5 DE-604 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018885343 | ||
Datensatz im Suchindex
| _version_ | 1804141018307624960 |
|---|---|
| adam_text | Contents
Preface
xv
1
Introduction
1
1.1
Neurons
................................... 1
1.1.1
What Is a Spike?
.......................... 2
1.1.2
Where Is the Threshold?
...................... 3
1.1.3
Why Are Neurons Different, and Why Do Wo Care?
....... 6
1.1.4
Building Models
........................... 6
1.2
Dynamical Systems
............................. 8
1.2.1
Phase Portraits
...........................
S
1.2.2
Bifurcations
............................. 11
1.2.3
Hodgkin
Classification
....................... 1-і
1.2.4
Neurocomputational properties
.................. IG
1.2.5
Building Models (Revisited)
.................... 20
Review of Important Concepts
.......................... 21
Bibliographical Notes
............................... 21
2
Electrophysiology of Neurons
25
2.1
Ions
..................................... 25
2.1.1
Xernst Potential
.......................... 26
2.1.2
Ionic Currents and Conductances
................. 27
2.1.3
Equivalent Circuit
......................... 28
2.1.4
Resting Potential and Input Resistance
.............. 29
2.1.5
Voltage-Clamp and I-V Relation
.................. 30
2.2
Conductances
................................ 32
2.2.1
Voltage-Gated Channels
...................... 33
2.2.2
Activation of Persistent Currents
................. 34
2.2.3
Inactivation of Transient Currents
................. 35
2.2.4
Hyperpolarizatiou-Activated Channels
.............. 36
2.3
The Hodgkm-Huxley Model
........................
ЗГ
2.3.1
Hodgkin-Huxley Equations
..................... 37
2.3.2
Action Potential
.......................... 41
2.3.3
Propagation of the Action Potentials
............... 42
vili
ΠλΥ7/·;. ΎΝ
2.3.4
Dominiu·
(. опц)аі Тшгіи>
......................
К!
2.3.5
Summary of
Yolta^e-Gaîed
Cnnvut^-
...............
Ii
Review of Important Concepts
..........................
1!>
Bibliographical
Xotes
...............................
-»Π
Exercises
......................................
»tl
One-Dimensional Systems
53
3.1
Electrophysiological Examples
.......................
:>3
3.1.1
I-V Relations and Dynamics
.................... 51
3.1.2
Leak
+
Instantaneous Isa.p
.................... ·*
3.2
Dynamical Systems
............................. 57
3.2.1
Geometrical Analysis
........................ 59
3.2.2
Equilibria
.............................. 00
3.2.3
Stability
............................... (¡0
3.2.4
Eigenvalues
............................. 01
3.2.5
Unstable Equilibria
......................... (51
3.2.6
Attraction Domain
......................... 02
3.2.7
Threshold and Action Potential
.................. 03
3.2.8
Bistability and Hysteresis
..................... 0(5
3.3
Phase Portraits
............................... 07
3.3.1
Topological Equivalence
......................
(>H
3.3.2
Local Equivalence and the Hartmaii-Grobmaii Theorem
..... 09
3.3.3
Bifurcations
............................. 70
3.3.4
Saddle-Node (Fold) Bifurcation
.................. 74
3.3.5
Slow Transition
........................... 75
3.3.6
Bifurcation Diagram
........................ 77
3.3.7
Bifurcations and I-V Relations
................... 77
3.3.8
Quadratic Integrate-and-Fire Neuron
...............
HO
Review of Important Concepts
.......................... 82
Bibliographical Notes
............................... 83
Exercises
...................................... 83
Two-Dimensional Systems
89
4.1
Planar Vector Fields
............................ 89
4.1.1
Nullclines
.............................. 92
4.1.2
Trajectories
............................. 94
4.1.3
Limit Cycles
............................. 96
4.1.4
Relaxation Oscillators
....................... 98
4.2
Equilibria
.................................. 9!)
4.2.1
Stability
................................100
4.2.2
Local Linear Analysis
........................ 101
4.2.3
Eigenvalues and Eigenvectors
................... 102
4.2.4
Local Equivalence
.......................... 103
СШТЕЅТЅ
ix
4.2.5
Classification
of Equilibria
..................... 103
4.2.6
Example: FitzHugh-Nagunio Model
................ 106
4.3
Phase Portraits
............................... 108
1.3.1
Bistability and Attraction Domains
................ 108
4.3.2
Stable/ Unstable Manifolds
..................... 109
4.3.3
Hoinoclinic/Heteroclime Trajectories
...............
Ill
4.3.4
Saddle-Node Bifurcation
...................... 113
4.3.5
Andronov-
Hopf
Bifurcation
.................... 116
Review of Important Concepts
.......................... 121
Bibliographical
Xotes
............................... 122
Exercises
...................................... 122
5
Conductance-Based Models and Their Reductions
127
5.1
Minimal Models
............................... 127
5.1.1
Amplifying and Resonant Gating Variables
............ 129
5.1.2
І^р+Ік-Моаеі
........................... 132
5.1.3
/Na.t-model
............................. 133
5.1.4
JWp+Jh-Model
........................... 136
5.1.5
4+JKir-Model
............................ 138
5.1.6
ік+ікіг-Мосієі
........................... 140
5.1.7
/A-Model
.............................. 142
5.1.8
Ca^-Gated Minimal Models
.................... 147
5.2
Reduction of Multidimensional Models
.................. 147
5.2.1
Hodgkin-Huxley model
....................... 147
5.2.2
Equivalent Potentials
........................ 151
5.2.3
Nullclines and I-V Relations
....................
loi
5.2.4
Reduction to Simple Model
.................... 153
Review of Important Concepts
.......................... 156
Bibliographical Notes
............................... 156
Exercises
...................................... 157
6
Bifurcations
159
6.1
Equilibrium (Rest State)
.......................... 159
6.1.1
Saddle-Node (Fold)
......................... 162
6.1.2
Saddle-Node on Invariant Circle
.................. 164
6.1.3
Supercritical Andronov-Hopf
.................... 168
6.1.4
Subcriticai
Andronov-Hopf
..................... 174
6.2
Limit Cycle (Spiking State)
........................ 178
6.2.1
Saddle-Node on Invariant Circle
.................. 180
6.2.2
Supercritical Andronov-Hopf
.................... 181
6.2.3
Fold Limit Cycle
.......................... 181
6.2.4
Homocliuic
............................. 185
6.3
Other Interesting Cases
........................... 190
CONTENTS
6.3.1
Three-Dimensional
Phase Space.................. 190
6.3.2
Cusp and Pitchfork
......................... 192
6.3.3 Bogdanov-Takens.......................... 194
6.3.4
Relaxation Oscillators and Canards
................ 198
6.3.5
Bautin
................................ 200
6.3.6
Saddle-Node Homoclinic Orbit
................... 201
6.3.7
Hard and Soft Loss of Stability
.................. 204
Bibliographical Notes
............................... 205
Exercises
...................................... 210
Neuronal
Excitability
215
7.1
Excitability
................................. 215
7.1.1
Bifurcations
............................. 216
7.1.2
Hodgkin s Classification
...................... 218
7.1.3
Classes
1
and
2........................... 221
7.1.4
Class
3................................ 222
7.1.5
Ramps, Steps, and Shocks
..................... 224
7.1.6
Bistability
.............................. 226
7.1.7
Class
1
and
2
Spiking
........................ 228
7.2
Integrators vs. Resonators
......................... 229
7.2.1
Fast Subthreshold Oscillations
................... 230
7.2.2
Frequency Preference and Resonance
............... 232
7.2.3
Frequency Preference in Vivo
................... 237
7.2.4
Thresholds and Action Potentials
................. 238
7.2.5
Threshold manifolds
........................ 240
7.2.6
Rheobase
.............................. 242
7.2.7
Postinhibitory Spike
........................ 242
7.2.8
Inhibition-Induced Spiking
..................... 244
7.2.9
Spike Latency
............................ 246
7.2.10
Flipping from an Integrator to a Resonator
............ 248
7.2.11
Transition Between Integrators and Resonators
......... 251
7.3
Slow Modulation
.............................. 252
7.3.1
Spike Frequency Modulation
.................... 255
7.3.2
I-V Relation
............................. 256
7.3.3
Slow Subthreshold Oscillation
................... 258
7.3.4
Rebound Response and Voltage Sag
................ 259
7.3.5
ΑΗΡ
and ADP
........................... 260
Review of Important Concepts
.......................... 264
Bibliographical Notes
............................... 264
Exercises
...................................... 265
CONTENTS xi
8 Simple Models 267
8.1
Simplest
Models............................... 267
8.1.1 Integrate-and-Fire ......................... 268
8.1.2 Resonate-and-Fire ......................... 269
8.1.3
Quadratic
Integrate-and-Fire.................... 270
8.1.4 Simple Model
of Choice ......................
272
8.1.5
Canonical
Models.......................... 278
8.2
Cortex
.................................... 281
8.2.1
Regular Spiking
(RS)
Neurons
................... 282
8.2.2
Intrinsically Bursting (IB) Neurons
................ 288
8.2.3
Multi-Compartment Dendritic Tree
................ 292
8.2.4
Chattering (CH) Neurons
..................... 294
8.2.5
Low-Threshold Spiking
(LTS) Interneurons............
296
8.2.6
Fast Spiking (FS)
Interneurons
.................. 298
8.2.7
Late Spiking (LS) Interneurons
.................. 300
8.2.8
Diversity of Inhibitory Interneurons
................ 301
8.3
Thalamus
.................................. 304
8.3.1
Thalamocortical (TC) Relay Neurons
............... 305
8.3.2
Reticular
Thalamic Nucleus (RTN) Neurons
........... 306
8.3.3
Thalamic Interneurons
....................... 308
8.4
Other Interesting Cases
........................... 308
8.4.1
Hippocainpal
CAI
Pyramidal Neurons
.............. 308
8.4.2
Spiny Projection Neurons of Neostriatum and Basal Ganglia
. . 311
8.4.3
Mesencephalic V Neurons of Brainstem
.............. 313
8.4.4
Stellate Cells of Entorhinal Cortex
................ 314
8.4.5
Mitral Neurons of the Olfactory Bulb
............... 316
Review of Important Concepts
.......................... 319
Bibliographical Notes
............................... 319
Exercises
...................................... 321
9
Bursting
325
9.1
Electrophysiology
.............................. 325
9.1.1
Example: The INa,p+JK+/K(M)-Model
............... 327
9.1.2
Fast-Slow Dynamics
........................ 329
9.1.3
Minimal Models
........................... 332
9.1.4
Central Pattern Generators and Half-Center Oscillators
..... 334
9.2
Geometry
.................................. 335
9.2.1
Fast-Slow Bursters
......................... 336
9.2.2
Phase Portraits
........................... 336
9.2.3
Averaging
.............................. 339
9.2.4
Equivalent Voltage
......................... 341
9.2.5
Hysteresis Loops and Slow Waves
................. 342
9.2.6
Bifurcations Resting
<-►
Bursting
<-»
Tonic Spiking
...... 344
xii CONTENTS
9.3
Classification
................................ 347
9.3.1 Fold/Homoclinic .......................... 350
9.3.2 Circle/Circle............................. 354
9.3.3 SubHopf/Fold
Cycle
........................ 359
9.3.4
Fold/Fold Cycle
........................... 364
9.3.5 Fold/Hopf.............................. 365
9.3.6
Fold/Circle
............................. 366
9.4 Neurocomputational
Properties
...................... 367
9.4.1
How to Distinguish?
........................ 367
9.4.2
Integrators vs. Resonators
..................... 368
9.4.3
Bistability
.............................. 368
9.4.4
Bursts as a Unit of
Neuronal
Information
............. 371
9.4.5
Chirps
................................ 372
9.4.6
Synchronization
........................... 373
Review of Important Concepts
.......................... 375
Bibliographical Notes
............................... 376
Exercises
...................................... 378
10
Synchronization
385
Solutions to Exercises
387
References
419
Index
435
10
Synchronization (www.izhikevich.com)
443
10.1
Pulsed Coupling
............................... 444
10.1.1
Phase of Oscillation
......................... 444
10.1.2
Isochrons
.............................. 445
10.1.3
PRC
................................. 446
10.1.4
Type
0
and Type
1
Phase Response
................ 450
10.1.5
Poincare Phase Map
........................ 452
10.1.6
Fixed points
............................. 453
10.1.7
Synchronization
........................... 454
10.1.8
Phase-Locking
............................ 456
10.1.9
Arnold Tongues
........................... 456
10.2
Weak Coupling
............................... 458
10.2.1
Winfree s Approach
......................... 459
10.2.2
Kuramoto s Approach
....................... 460
10.2.3
Malkin s Approach
......................... 461
10.2.4
Measuring PRCs Experimentally
................. 462
10.2.5
Phase Model for Coupled Oscillators
............... 465
10.3
Synchronization
............................... 467
CONTENTS xiii
10.3.1
Two Oscillators
........................... 469
10.3.2
Chains
................................ 471
10.3.3
Networks
.............................. 473
10.3.4
Mean-Field Approximations
.................... 474
10.4
Examples
.................................. 475
10.4.1
Phase Oscillators
.......................... 475
10.4.2
SNIC Oscillators
.......................... 477
10.4.3
Homoclinic Oscillators
....................... 482
10.4.4
Relaxation Oscillators and FTM
.................. 484
10.4.5
Bursting Oscillators
......................... 486
Review of Important Concepts
.......................... 488
Bibliographical Notes
............................... 489
Solutions
...................................... 497
|
| any_adam_object | 1 |
| author | Ižikevič, Eugene M. 1967- |
| author_GND | (DE-588)137452446 |
| author_facet | Ižikevič, Eugene M. 1967- |
| author_role | aut |
| author_sort | Ižikevič, Eugene M. 1967- |
| author_variant | e m i em emi |
| building | Verbundindex |
| bvnumber | BV035992660 |
| callnumber-first | Q - Science |
| callnumber-label | QP355 |
| callnumber-raw | QP355.2 |
| callnumber-search | QP355.2 |
| callnumber-sort | QP 3355.2 |
| callnumber-subject | QP - Physiology |
| classification_rvk | WC 7700 SK 950 WW 2200 CZ 1300 ST 300 |
| ctrlnum | (OCoLC)457159828 (DE-599)BVBBV035992660 |
| dewey-full | 612.8 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 612 - Human physiology |
| dewey-raw | 612.8 |
| dewey-search | 612.8 |
| dewey-sort | 3612.8 |
| dewey-tens | 610 - Medicine and health |
| discipline | Biologie Informatik Psychologie Mathematik Medizin |
| edition | 1. MIT Press paperback ed. |
| format | Book |
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| id | DE-604.BV035992660 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:09:12Z |
| institution | BVB |
| isbn | 0262514206 9780262514200 9780262090438 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018885343 |
| oclc_num | 457159828 |
| open_access_boolean | |
| owner | DE-20 DE-11 DE-188 DE-355 DE-BY-UBR DE-703 DE-83 DE-19 DE-BY-UBM |
| owner_facet | DE-20 DE-11 DE-188 DE-355 DE-BY-UBR DE-703 DE-83 DE-19 DE-BY-UBM |
| physical | XVI, 441 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | MIT Press |
| record_format | marc |
| series2 | Computational neuroscience |
| spelling | Ižikevič, Eugene M. 1967- Verfasser (DE-588)137452446 aut Dynamical systems in neuroscience the geometry of excitability and bursting Eugene M. Izhikevich 1. MIT Press paperback ed. Cambridge, Mass. [u.a.] MIT Press 2010 XVI, 441 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computational neuroscience In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum--or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. Differentiable dynamical systems Models, Neurological Nerve Net physiology Neurology Neurons Neurons physiology Neurosciences Nonlinear Dynamics Neurowissenschaften (DE-588)7555119-6 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Neurowissenschaften (DE-588)7555119-6 s Dynamisches System (DE-588)4013396-5 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018885343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ižikevič, Eugene M. 1967- Dynamical systems in neuroscience the geometry of excitability and bursting Differentiable dynamical systems Models, Neurological Nerve Net physiology Neurology Neurons Neurons physiology Neurosciences Nonlinear Dynamics Neurowissenschaften (DE-588)7555119-6 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)7555119-6 (DE-588)4013396-5 |
| title | Dynamical systems in neuroscience the geometry of excitability and bursting |
| title_auth | Dynamical systems in neuroscience the geometry of excitability and bursting |
| title_exact_search | Dynamical systems in neuroscience the geometry of excitability and bursting |
| title_full | Dynamical systems in neuroscience the geometry of excitability and bursting Eugene M. Izhikevich |
| title_fullStr | Dynamical systems in neuroscience the geometry of excitability and bursting Eugene M. Izhikevich |
| title_full_unstemmed | Dynamical systems in neuroscience the geometry of excitability and bursting Eugene M. Izhikevich |
| title_short | Dynamical systems in neuroscience |
| title_sort | dynamical systems in neuroscience the geometry of excitability and bursting |
| title_sub | the geometry of excitability and bursting |
| topic | Differentiable dynamical systems Models, Neurological Nerve Net physiology Neurology Neurons Neurons physiology Neurosciences Nonlinear Dynamics Neurowissenschaften (DE-588)7555119-6 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Differentiable dynamical systems Models, Neurological Nerve Net physiology Neurology Neurons Neurons physiology Neurosciences Nonlinear Dynamics Neurowissenschaften Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018885343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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