I am an assistant professor in the Department of Mathematics (Amsterdam Center for Dynamics and Computation) at Vrije Universiteit Amsterdam.
My research is on nonlinear dynamical systems: normal forms, versal deformations, and decompositions of singular vector fields using sl(2)-representation theory. Currently I focus on normal forms and bifurcations of network dynamical systems, in particular feed-forward and colored networks.
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 AmsterdamResearch interests:
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." Nonlinearity, Volume 38, Number 9. https://iopscience.iop.org/article/10.1088/1361-6544/ae0289
F. Mokhtari, Jesús Palacián, Patricia Yanguas. "Bifurcations of Riemann Ellipsoids." under press: SIAM Journal on Applied Dynamical Systems, 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." 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 Science
M. 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 projects
I welcome BSc and MSc students interested in network dynamical systems, equivariant dynamics and bifurcation analysis. Current projects: "Group Actions and Equivariant Dynamics" (BSc) and "Algebraic Structure of Coupled Cell Networks" (MSc). Feel free to contact me.
Mathematical Modelling of Dynamical Systems (Mathematics)-Spring(2024)
Calculus (ME) (VU-UTwente) https://www.utwente.edu/en/bachelor-mechanical-engineering-vu-ut/ Lecturer(2022)
Vector Calculus (MNW-VU) Lecturer and tutorial Feb-Mar 2020.
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 Analytics-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 — Isfahan University of Technology (IUT), September 2013.
CV
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
Chair of the OLC Committee for the Medical Natural Sciences (Medische Natuurwetenschappen) program. You can find more information about the program here: Bachelor and Master Program.
ICT Committee member: representative of the mathematics department
Organizer of the mini-symposium "Stability and Bifurcations of Hamiltonian Systems", XLIV Dynamics Days Europe, Bremen, 2024
Organizer of "ACDC at SIAM 2025", a one-day workshop of the Amsterdam Center for Dynamics and Computation, VU Amsterdam, May 2025
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.
MSc Applied Mathematics (Dynamical Systems), Isfahan University of Technology.
BSc Pure Mathematics at the Department of Mathematics University of Isfahan.
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.