Fahimeh Mokhtari

I am an assistant professor at the Department of Mathematics

(Amsterdam Center for Dynamics and Computation) at Vrije Universiteit Amsterdam.

My research so far focused on the study of the nonlinear differential equations, in particular, the normal form of nonlinear dynamical systems, versal deformation, and decomposition of the singular dynamical systems using Sl(2)-representation theory. At the moment my research has a strong focus on the study of the normal form and bifurcation of network dynamical systems of types feed-forward and colored.

Contact: Fahimeh Mokhtari فهیمه مختاری

Email: f.mokhtari/vu/nl

Office: 9A-59 (NU BUILDING)

Postal address: Vrije Universiteit AmsterdamDepartment of MathematicsNIEUW UNIVERSITEITSGEBOUW De Boelelaan 11111081 HV Amsterdam

Research interests:

Dynamical Systems and Representation Theory Network Dynamical SystemsNormal Form TheoryHamiltonian SystemsBifurcation TheorySymbolic ComputationsSingularity Theory

Projects and Preprints:

Network Dynamical Systems

"Lie Algebraic Structure of Nilpotent Feedforward (Single Nodes) Network Dynamical Systems"

"Lie Algebraic Structure of Nilpotent Feedforward (Block Forms) Network Dynamical Systems"

Riemann Ellipsoid

"Bifurcation of Riemann Ellipsoid and Nonlinear Stability"

Triple-zero Bifurcation

"On the Bifurcation, Blow-up, and Unfolding of Triple-Zero Singularities"

Publications:

F. Mokhtari, "Nilpotent Feed Forward Network Dynamics." arxiv.org/abs/2408.07447
F. Mokhtari, Jesús Palacián, Patricia Yanguas. "Bifurcations of Riemann Ellipsoids." arXiv:2306.04258
F. Mokhtari, J.A. Sanders. "The Lie algebraic structure of colored networks." arXiv:2109.11419
F. Mokhtari, E. Roell, J.A. Sanders. "Normal form for maps with nilpotent linear part." Accepted in Proceedings A. arXiv:2003.01568
F. Mokhtari, J.A. Sanders. "Equivariant decomposition of polynomial vector fields." Journal of Communications in Contemporary Mathematics, 17 September 2020. arXiv:1909.06955
F. Mokhtari, J.A. Sanders. "Versal Normal Form for Nonsemisimple Singularities." Journal of Differential Equations, Volume 267, Issue 5, 15 August 2019, Pages 3083-3113. ScienceDirect
F. Mokhtari. "On the representations and Z2 equivariant normal form of solenoidal Hopf–zero singularities." Physica D: Nonlinear Phenomena, Volumes 386–387, Pages 14-22, 2019. arXiv:1903.09892
M. Gazor, F. Mokhtari, J.A. Sanders. "Vector potential normal forms for solenoidal nilpotent singularities." Journal of Differential Equations, Volume 267, 407-442, 2019. arXiv:1711.09126
M. Gazor, F. Mokhtari. "Normal Forms of Hopf–Zero singularity." Nonlinearity, Volume 28, 311–330, 2015. IOP Science
M. Gazor, F. Mokhtari. "Volume-preserving normal forms of Hopf–Zero singularity." Nonlinearity, Volume 26, 2809–2832, 2013. IOP ScienceM. Gazor, F.
Mokhtari, J.A. Sanders. "Normal forms for Hopf–Zero singularities with nonconservative nonlinear part." Journal of Differential Equations, Volume 254, 1571–1581, 2013. ScienceDirect

Teaching

Student's project

Feel free to contact me if you would like to carry out a research project (BSc/MSc) in the direction of the Network Dynamical System, Bifurcation Analysis of triple-zero singularities.

Mathematical Modelling of Dynamical Systems (Mathematics)-Spring(2024)
Calculus (ME) (VU-UTwente) https://www.utwente.edu/en/bachelor-mechanical-engineering-vu-ut/ Lecturer(2022)
Mentoring projects of first-year BSc mechanical engineering students-(VU-UTwente) (Spring 2022/Spring 2021/Fall 2020)
Differential Equation (ME-IUT/MNW-VU) Lecturer (Fall 2017/Spring 2020/Spring 2021/Fall 2021/Fall 2022, Fall 2023 (first block))
Dynamical System (AUC) Lecturer (Fall 2020/Fall 2021/Fall 2022)

Analysis II (School of Business and Economics-VU) Lecturer Feb-Mar (2021)

Vector Calculus (MNW-VU) Lecturer and tutorial Feb-Mar2020.
From 2019 to 2020 I assisted in several courses such as Dynamical Systems (Math-VU), Numerical Methods (Math-VU), Single variable calculus (Math-VU)Tutorial and Extra help section, Dynamics and Computation (Business analytic-VU), Partial differential equations (Math-VU/UvA), and Vector calculus (MNW-VU)

Tutorial teacher for international students (Math-IUT) In cooperation with the International and Scientific Cooperation Office at Isfahan University of Technology, Fall and Winter 2017. (Master course)

Singularity Theory (Math-IUT)Teaching assistant Fall 2013. (Master course)

Complex Analysis Teaching assistant (Math-IUT) Winter 2014–Spring 2015.

Bachelor thesis: The Homoclinic Melnikov Method — Thibault Lim, 2025.
Bachelor thesis: Network Dynamical Systems — Sofia Vida Martin, 2025.
Bachelor thesis: Blow-up Method: Theory and Applications — Irini Papathanasiadi, 2025.
Master project (co-supervision): Parameter-dependent Normal Forms for Maps — Ernst Röell, Utrecht University, February 2020.
Bachelor thesis: Conjugate Phase Portraits of Linear Systems — Islamic University of Technology (IUT), September 2013.

Employment History:

February 2019 - Present: Assistant Professor at the Department of Mathematics, Faculty of Sciences, VU Amsterdam
March 2018 – February 2019: Visiting Researcher at the Department of Mathematics, Faculty of Sciences, VU Amsterdam
September 2012 – June 2018: Ph.D. in Applied Mathematics (Dynamical Systems) from Isfahan University of Technology

Service:

Chair of the OLC Committee for the Medical Natural Science (Medische Natuurwetenschappen) program. You can find more information about the program here: Bachelor and Master Program.
ICT Committee member: Representative of the math department

https://vu.nl/nl/medewerker/beta-wegwijzer/it-commissie-beta

Previously: Co-organizer of the general math colloquium at VU Amsterdam

Education:

Ph.D. Applied Mathematics (Dynamical Systems), Isfahan University of Technology.

Thesis title: “Normal Form of Some Three-Dimensional Singular Vector Fields" September 2012-June 2018.

M. Sc . Applied Mathematics (Dynamical Systems), Isfahan University of Technology.

Thesis title: “Normal Form of Hopf-Zero Singular Vector Fields" September 2009-September 2011.

BSc Pure Mathematics at the Department of Mathematics University of Isfahan.

September 2005-June 2009.
Awards:

Awarded a scholarship by the Ministry of Science, Research and Technology of Iran to conduct research at the University of Utrecht and Vrije Universiteit, Amsterdam (2015-2016).
Received grants for research projects from the Presidency of the Islamic Republic of Iran National Elites Foundation (2014).
Recognized as a "distinguished student" in scientific competitions among all students at Isfahan University of Technology (2016).
Second laureate of the "Khwarizmi Youth Award" in the "Fundamental Researches" Section, Tehran, Iran (2013).
Ranked among the top ten percent of distinguished students (2005-2009).
Recognized as a distinguished student at the University of Isfahan (2005-2009).
Second rank in Pure Math, B.Sc., at the Department of Mathematical Sciences, University of Isfahan, UI (2005-2009).
Second rank in Applied Math (Dynamical System), M.Sc., at the Department of Mathematical Sciences, Isfahan University of Technology, IUT (2009-2011).
First rank in Applied Math (Dynamical System), Ph.D., at the Department of Mathematical Sciences, Isfahan University of Technology, IUT.

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