Publications
Titles link to the published version while, when possible, links to the arXiv version.
name indicates a PhD student under my (co)supervision
Preprints:

Strategic control for a Boltzmann like decisionmaking model
(with L. VenegasPineda, M. Engel, J. Heitzig, M. Eser, and M. Cao)

On the analysis of a higherorder LotkaVolterra model: an application of Stensors and the polynomial complementarity problem
(with S. Cui, Q, Zhao, G. Zhang, and M. Cao)
Abstract It is known that the effect of species' density on species' growth is nonadditive in real ecological systems. This challenges the conventional LotkaVolterra model, where the interactions are always pairwise and their effects are additive. To address this challenge, we introduce HOIs (HigherOrder Interactions) which are able to capture, for example, the indirect effect of one species on a second one correlating to a third species. Towards this end, we propose a general higherorder LotkaVolterra model. We provide an existence result of a positive equilibrium for a nonhomogeneous polynomial equation system with the help of Stensors. Afterward, by utilizing the latter result, as well as the theory of monotone systems and results from the polynomial complementarity problem, we provide comprehensive results regarding the existence, uniqueness, and stability of the corresponding equilibrium. These results can be regarded as natural extensions of many analogous ones for the classical LotkaVolterra model, especially in the case of full cooperation, competition among two factions, and pure competition. Finally, illustrative numerical examples are provided to highlight our contributions. 
Ergodicity in planar slowfast systems through slow relation functions
(with R. Huzak and C. Kuehn) 
On Metzler positive systems on hypergraphs
(with S. Cui, G. Zhang, and M. Cao) 
On network dynamical systems with a nilpotent singularity
(with C. Kuehn) 
General SIS diffusion process with direct and indirect spreading on a hypergraph
(with S. Cui, F. Liu, and M. Cao) 
Nonlinear Laplacian Dynamics: Symmetries, Perturbations, and Consensus
(with R. Bonetto) 
The hyperbolic umbilic singularity in fastslow systems
(with C. Kuehn and M. Steinert)
Journals:

On discretetime polynomial dynamical systems on hypergraphs
(with S. Cui, G. Zhang, and M. Cao)
IEEE LCSS, 2024 
Persistent synchronization of heterogeneous networks with timedependent linear diffusive coupling
(with C. Kuehn and I. Longo)
SIAM Journal of Applied Dynamical Systems 
Discretetime Layerednetwork Epidemics Model with Timevarying Transition Rates and Multiple Resources
(with S. Cui, F. Liu, and M. Cao)
Automatica, 2024 
Stable Chimera States: A Geometric Singular Perturbation Approach
(with L. Venegas and M. Cao)
Chaos, 2023 
Simulationbased Reconstructed Diffusion provides accurate values of mobility in confined spaces, unveiling the effect of aging in Escherichia coli
(with L. Mantovanelli, D. S. Linnik, M. Punter, W. M. Smigiel, and B. Poolman)
PLoS Comput Biol. 2023 
Slowfast torus knots
(with R. Huzak)
Bull. Belgian Math. Soc., 2022. 
A geometric analysis of the SIRS epidemiological model on a homogeneous network
(with C. Kuehn, A. Pugliese, and M. Sensi)
Journal of Theoretical Biology, 2021. 
Controlling canard cycles
(with C. Kuehn)
Journal of Dynamical and Control Systems, 2021. 
A geometric analysis of the SIR, SIRS and SIRWS epidemiological models
(with C. Kuehn, A. Pugliese and M. Sensi)
Nonlinear Analysis: Real World Applications, 2021. 
Geometric analysis of Oscillations in the Frzilator model
(with H. Tafgvafarad, P. Szmolyan and M. Cao)
Journal of Mathematical Analysis and Applications, 2021. 
Extended and symmetric loss of stability for canards in planar fastslow maps
(with M. Engel)
SIAM Journal on Applied Dynamical Systems, 2020. 
On Fast–Slow Consensus Networks with a Dynamic Weight
(with C. Kuehn)
Journal of Nonlinear Science, 2020. 
Stabilization of a class of slowfast control systems at nonhyperbolic points
(with 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
(with J. M. A. Scherpen)
IEEE Control Systems Letters, 2018. 
Parameterrobustness analysis for a biochemical oscillator model describing the socialbehavior transition phase of myxobacteria
(with H. Tafgvafarad 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
(with J. M. A. Scherpen)
IEEE Control Systems Letters, 2017. 
Limit sets within curves where trajectories converge to
(with P. Ramazi and M. Cao)
Applied Mathematics Letters, 2017. 
Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach
(with J. Collado).
Applied Mathematics, 2016. 
Analysis of a slow fast system near a cusp singularity
(with H. W. Broer and R. Roussarie)
Journal of Differential Equations, 2016. 
Formal normal form of Ak slowfast systems
Comptes Rendus Mathematique, 2015. 
Bifurcations of a nongravitational interaction problem
(with X. Liu)
Applied Mathematics and Computation, 2015. 
Polynomial normal forms of Constrained Differential Equations with three parameters
(with H. W. Broer)
Journal of Differential Equations, 2014.
Conference proceedings:

Species Coexistence and Extinction Resulting from Higherorder LotkaVolterra TwoFaction Competition
(with S. Cui, Q. Zhao and M. Cao)
62nd IEEE Conference on Decision and Control, 2023 
A topological perspective on singular canards for critical sets with transverse intersections
(with R. Bonetto) 
A survey on the blowup method for fastslow systems ,
(with C. Kuehn)
Contemporary Mathematics, 2021, 775, pp. 115–160.  Nonlinear adaptive stabilization of a class of planar slowfast systems at a nonhyperbolic point
(with J. M. A. Scherpen and D. del PuertoFlores)
American Control Conference 2017.  Stabilization of a planar slowfast system at a nonhyperbolic point
(with J. M. A. Scherpen)
Mathematical Theory of Networks and Systems 2016.  Model order reduction of a flexiblejoint robot: a portHamiltonian approach
(with 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
(with R. MartínezMartínez, J. A. León and G. FernándezAnaya)
Congreso de la Asociación de México de Control Automático, 2009.