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 subprocess 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 phasespace 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. JardónKojakhmetov and C. Kuehn.
@article{jardon2019controlling, title={Controlling Canard Cycles}, author={JardonKojakhmetov, Hildeberto and Kuehn, Christian}, journal={arXiv preprint arXiv:1911.11861}, year={2019} }
Journals:
*Clicking on the title takes you to the Publisher’s version.
Geometric analysis of Oscillations in the Frzilator model [arXiv]
H. Tafgvafarad, H. JardónKojakhmetov, P. Szmolyan and M. Cao.
Accepted / to appear in Journal of Mathematical Analysis and Applications. 
A geometric analysis of the SIR, SIRS and SIRWS epidemiological models
H. JardónKojakhmetov, C. Kuehn, A. Pugliese and M. Sensi.
Nonlinear Analysis: Real World Applications, vol. 50, April 2021. 
Extended and symmetric loss of stability for canards in planar fastslow maps [arXiv]
M. Engel and H. JardónKojakhmetov.
Accepted / to appear in SIAM Journal on Applied Dynamical Systems, 2020. 
On Fast–Slow Consensus Networks with a Dynamic Weight
H. JardónKojakhmetov and Christian Kuehn.
Journal of Nonlinear Science, 2020. 
Stabilization of a class of slowfast control systems at nonhyperbolic points
[Preprint]
H. JardónKojakhmetov, J. M. A. Scherpen, and D. del PuertoFlores.
Automatica, 2019. 
Improving the region of attraction of a nonhyperbolic point in slowfast systems with one fast direction
[Preprint]
H. JardónKojakhmetov and J. M. A. Scherpen.
IEEE Control Systems Letters, 2018. 
Parameterrobustness analysis for a biochemical oscillator model describing the socialbehavior transition phase of myxobacteria
H. Tafgvafarad, H. JardónKojakhmetov, and M. Cao.
Proceedings of the Royal Society A, 2018. 
Model order reduction and composite control for a class of slowfast systems around a nonhyperbolic point [Preprint]
H. JardónKojakhmetov and J. M. A. Scherpen.
IEEE Control Systems Letters, 2017. 
Limit sets within curves where trajectories converge to
P. Ramazi, H. JardónKojakhmetov and M. Cao.
Applied Mathematics Letters, 2017. 
Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach
J. Collado and H. JardónKojakhmetov.
Applied Mathematics, 2016. 
Analysis of a slow fast system near a cusp singularity [arXiv]
H. JardónKojakhmetov, H. W. Broer and R. Roussarie.
Journal of Differential Equations, 2016. 
Formal normal form of Ak slowfast systems [arXiv]
H. JardónKojakhmetov.
Comptes Rendus Mathematique, 2015. 
Bifurcations of a nongravitational interaction problem
X. Liu and H. JardónKojakhmetov.
Applied Mathematics and Computation, 2015. 
Polynomial normal forms of Constrained Differential Equations with three parameters [arXiv]
H. JardónKojakhmetov and H. W. Broer.
Journal of Differential Equations, 2014.
Conference proceedings:

A survey on the blowup method for fastslow systems [arXiv],
H. JardónKojakhmetov and C. Kuehn.
Accepted/to appear in Contemporary Mathematics (of the American Mathematical Soc.), 2019.  Nonlinear adaptive stabilization of a class of planar slowfast systems at a nonhyperbolic point
H. JardónKojakhmetov, J. M. A. Scherpen and D. del PuertoFlores.
American Control Conference 2017.  Stabilization of a planar slowfast system at a nonhyperbolic point
H. JardónKojakhmetov and J. M. A. Scherpen.
Mathematical Theory of Networks and Systems 2016.  Model order reduction of a flexiblejoint robot: a portHamiltonian approach
H. JardónKojakhmetov, M. MunozArias and J. M. A. Scherpen.
IFAC Symposium on Nonlinear Control Systems 2016.  Estabilización de Redes Complejas Fraccionarias de Sistemas de Lorenz y Sistemas de Chen
R. MartínezMartínez, H. JardónKojakhmetov, J. A. León and G. FernándezAnaya
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 FernándezAnaya (U. Iberoamericana)  Pouria Ramazi 
Christian Kuehn (TUM)  Robert Roussarie (U. Bourgogne) 
Xia Liu  Hadi Taghvafard (U. Leiden) 
Rafael MartínezMartínez (UPIITAIPN)  
Mauricio MuñozArias (RUG)  
Dunstano del PuertoFlores (UdG) 