Research

Many complex phenomena have intrinsically many different time scales. A usual system’s approach to understand them is to separate the processes at each time scale hoping that information of each sub-process will provide enough insight on the overall dynamics. Sometimes this approach works well, especially when the time scale separation is, in some sense, global. There are instances, however, where such an approach is not possible. In this latter situation, the time scale separation does not persist across the phase-space and may induce intricate dynamics. The goal of my research is to understand systems with the aforementioned behavior and to control them. Most of the following articles show work in that direction.


Publications:

Submitted:

Controlling canard cycles [arXiv]
H. Jardón-Kojakhmetov and C. Kuehn.
  @article{jardon2019controlling,
  title={Controlling Canard Cycles},
  author={Jardon-Kojakhmetov, Hildeberto and Kuehn, Christian},
  journal={arXiv preprint arXiv:1911.11861},
  year={2019}
  }
Extended and symmetric loss of stability for canards in planar fast-slow maps [arXiv]
M. Engel and H. Jardón-Kojakhmetov.
  @article{engel2019extended,
  title={Extended and symmetric loss of stability for canards in planar fast-slow maps},
  author={Engel, Maximilian and Jard{\'o}n-Kojakhmetov, Hildeberto},
  journal={arXiv preprint arXiv:1912.10286},
  year={2019}
  }
A geometric analysis of the SIR, SIRS and SIRWS epidemiological models [arXiv]
H. Jardón-Kojakhmetov, C. Kuehn, A. Pugliese and M. Sensi.
  @article{jardon2020geometric,
  title={A geometric analysis of the SIR, SIRS and SIRWS epidemiological models},
  author={Jard{\'o}n-Kojakhmetov, Hildeberto and Kuehn, Christian and Pugliese, Andrea and Sensi, Mattia},
  journal={arXiv preprint arXiv:2002.00354},
  year={2020}
  }
Geometric analysis of Oscillations in the Frzilator model [arXiv]
H. Tafgvafarad, H. Jardón-Kojakhmetov, P. Szmolyan and M. Cao.
  @article{taghvafard2019geometric,
  title={Geometric analysis of Oscillations in the Frzilator model},
  author={Taghvafard, Hadi and Jardon-Kojakhmetov, Hildeberto and Szmolyan, Peter and Cao, Ming},
  journal={arXiv preprint arXiv:1912.00659},
  year={2019}
  }

Journals:

*Clicking on the title takes you to the Publisher’s version.
  1. On Fast–Slow Consensus Networks with a Dynamic Weight
    Hildeberto Jardón-Kojakhmetov, and Christian Kuehn.
    Journal of Nonlinear Science, 2020.
  2. Stabilization of a class of slow-fast control systems at non-hyperbolic points  [Preprint]
    H. Jardón-Kojakhmetov, J. M. A. Scherpen, and D. del Puerto-Flores.
    Automatica, 2019.
  3. Improving the region of attraction of a non-hyperbolic point in slow-fast systems with one fast direction [Preprint]
    H. Jardón-Kojakhmetov and J. M. A. Scherpen.
    IEEE Control Systems Letters, 2018.
  4. Parameter-robustness analysis for a biochemical oscillator model describing the social-behavior transition phase of myxobacteria
    H. Tafgvafarad, H. Jardón-Kojakhmetov, and M. Cao.
    Proceedings of the Royal Society A, 2018.
  5. Model order reduction and composite control for a class of slow-fast systems around a non-hyperbolic point [Preprint]
    H. Jardón-Kojakhmetov and J. M. A. Scherpen.
    IEEE Control Systems Letters, 2017.
  6. Limit sets within curves where trajectories converge to
    P. Ramazi, H. Jardón-Kojakhmetov and M. Cao.
    Applied Mathematics Letters, 2017.
  7. Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach
    J. Collado and H. Jardón-Kojakhmetov.
    Applied Mathematics, 2016.
  8. Analysis of a slow fast system near a cusp singularity [arXiv]
    H. Jardón-Kojakhmetov, H. W. Broer and R. Roussarie.
    Journal of Differential Equations, 2016.
  9. Formal normal form of Ak slow-fast systems [arXiv]
    H. Jardón-Kojakhmetov.
    Comptes Rendus Mathematique, 2015.
  10. Bifurcations of a non-gravitational interaction problem
    X. Liu and H. Jardón-Kojakhmetov.
    Applied Mathematics and Computation, 2015.
  11. Polynomial normal forms of Constrained Differential Equations with three parameters [arXiv]
    H. Jardón-Kojakhmetov and H. W. Broer.
    Journal of Differential Equations, 2014.

Conference proceedings:

  1. A survey on the blow-up method for fast-slow systems [arXiv],
    H. Jardón-Kojakhmetov and C. Kuehn.
    Accepted/to appear in Contemporary Mathematics (of the American Mathematical Soc.), 2019.
  2. Nonlinear adaptive stabilization of a class of planar slow-fast systems at a non-hyperbolic point
    H. Jardón-Kojakhmetov, J. M. A. Scherpen and D. del Puerto-Flores.
    American Control Conference 2017.
  3. Stabilization of a planar slow-fast system at a non-hyperbolic point
    H. Jardón-Kojakhmetov and J. M. A. Scherpen.
    Mathematical Theory of Networks and Systems 2016.
  4. Model order reduction of a flexible-joint robot: a port-Hamiltonian approach
    H. Jardón-Kojakhmetov, M. Munoz-Arias and J. M. A. Scherpen.
    IFAC Symposium on Nonlinear Control Systems 2016.
  5. Estabilización de Redes Complejas Fraccionarias de Sistemas de Lorenz y Sistemas de Chen
    R. Martínez-Martínez, H. Jardón-Kojakhmetov, J. A. León and G. Fernández-Anaya
    Congreso de la Asociación de México de Control Automático, 2009.

Collaborators:

I have had the great pleasure of working together with:

Henk Broer (RUG) Andrea Pugliese (U. Trento)
Ming Cao (RUG) Jacquelien Scherpen (RUG)
Joaquín Collado (CINVESTAV) Mattia Sensi (U. Trento)
Maximilan Engel (TUM) Peter Szmolyan (TU Wien)
Guillermo Fernández-Anaya (U. Iberoamericana) Pouria Ramazi
Christian Kuehn (TUM) Robert Roussarie (U. Bourgogne)
Xia LiuHadi Taghvafard (U. Leiden)
Rafael Martínez-Martínez (UPIITA-IPN)
Mauricio Muñoz-Arias (RUG)
Dunstano del Puerto-Flores (UdG)