MS05.1: Slow-Fast Systems and Phenomena

Session Information

Jul 24, 2024 09:00 - 11:00(Europe/Amsterdam)
Venue : AULA - Commissiekamer 3
20240724T0900 20240724T1100 Europe/Amsterdam MS05.1: Slow-Fast Systems and Phenomena AULA - Commissiekamer 3 Enoc2024 n.fontein@tudelft.nl Add to Calendar

Sub Sessions

Equation-free analysis of brain activity: Stability and bifurcation analysis of the striatum network

MS-05 - Slow-Fast Systems and Phenomena 09:00 AM - 09:20 AM (Europe/Amsterdam) 2024/07/24 07:00:00 UTC - 2024/07/24 07:20:00 UTC
The striatum brain nucleus is central for motor and cognitive functions. We propose a large-scale biophysical network for this part of the brain, using a modified Hodgkin-Huxley dynamics for neurons and a connectivity which is informed by a detailed human atlas. In this complex slow-fast system different spatio-temporal activity patterns emerge during healthy and pathological states (neurological disorder), depending on the intensity of the cortical inputs. Using equation-free methods and diffusion maps, we are able to identify a macroscopic order parameter. The equation-free approach enables a numerical analysis of the macroscopic dynamics of the striatum network. This includes a numerical bifurcation and stability analysis. Finally, the effect of deep brain stimulation on the spatiotemporal pattern formation in the network is discussed.
Presenters Jens Starke
Professor, University Of Rostock
Co-Authors
KS
Konstantinos Spiliotis
University Of Rostock
WJ
Wolfram Just
RK
Rüdiger Köhling

Upper Bound to the Response of Nonlinear Parametrically Excited Systems

MS-05 - Slow-Fast Systems and Phenomena 09:20 AM - 09:40 AM (Europe/Amsterdam) 2024/07/24 07:20:00 UTC - 2024/07/24 07:40:00 UTC
The upper bound response of Nonlinear Parametrically Excited (NPE) systems is investigated. Different systems including a NPE system under pure parametric excitation, a NPE system under interacting external excitation and a NPE cantilever beam with a tip mass are considered. In order to obtain the response of the system for the whole frequency range considered, the method of varying amplitudes (MVA) is used. Employing the MVA, analytical expressions for the displacement response of the system are derived. The MVA results are compared with analytical results of the Method of Multiple Scales (MMS) and the numerical results obtained from Direct Integration (DI) of the equation of motion, showing good agreement. In order to verify the MVA results in a practical application, experimental measurements of a Nonlinear Parametrically Excited Cantilever Beam (NPECB) with a tip mass are taken, demonstrating good agreement between experiments, theory and numerical findings.
Presenters
BM
Brian Mace
Emeritus Professor, University Of Auckland
Co-Authors Mehrdad Aghamohammadi
The University Of Auckland
VS
Vladislav Sorokin
The University Of Auckland

Uncovering slowly varying amplitudes from response measurements of nonlinear oscillators

MS-05 - Slow-Fast Systems and Phenomena 09:40 AM - 10:00 AM (Europe/Amsterdam) 2024/07/24 07:40:00 UTC - 2024/07/24 08:00:00 UTC
Nonlinear oscillatory behavior is commonly described in terms of amplitudes, phases, and frequencies. Only in rare cases, these quantities are constant and can be readily obtained via Fourier transformation. In many measurements of, for example, ocean waves, mechanical systems, and biological systems, the amplitudes and frequencies vary slowly in time. In this presentation, the authors present a strategy to decompose measurements of nonlinear oscillations into oscillations with slowly varying amplitudes and frequencies. The amplitude and frequency variations reveal fundamental insights into the observed oscillations and can be leveraged to derive modulation equations. These equations can be used to predict the oscillatory behavior when small perturbations are added. The capabilities of the proposed methodology are demonstrated using measurements from a nonlinear mechanical oscillator experiment.
Presenters
TB
Thomas Breunung
PostDoc, University Of Maryland, College Park
Co-Authors
BB
Balakumar Balachandran
Professor, University Of Maryland, College Park
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Session Participants

Online
Session speakers, moderators & attendees
PostDoc
,
University Of Maryland, College Park
Emeritus Professor
,
University Of Auckland
Professor
,
University Of Rostock
Assistant Professor
,
TU Delft
Post-doctoral researcher
,
Delft University Of Technology
Mr. Moslem Molaie Emamzadeh
PhD student
,
University Of Modena And Reggio Emilia
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Extendend Abstracts

1712076240SlowAmplEqu_R1.pdf
Uncovering slowly varying amplitudes ...
6
Submitted by Thomas Breunung
1712547748enoc2024ExtendedAbstract.pdf
Upper Bound to the Response of Nonli...
5
Submitted by Mehrdad Aghamohammadi
1705357245enoc-abstract24-JS-KS.pdf
Equation-free analysis of brain activ...
4
Submitted by Jens Starke

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