Titles link to the published version while, when possible, links to the arXiv version.

name indicates a PhD student under my (co-)supervision

Pre-prints:

  1. Strategic control for a Boltzmann like decision-making model
    (with L. Venegas-Pineda, M. Engel, J. Heitzig, M. Eser, and M. Cao)
  2. On the analysis of a higher-order Lotka-Volterra model: an application of S-tensors 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 non-additive in real ecological systems. This challenges the conventional Lotka-Volterra model, where the interactions are always pairwise and their effects are additive. To address this challenge, we introduce HOIs (Higher-Order 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 higher-order Lotka-Volterra model. We provide an existence result of a positive equilibrium for a non-homogeneous polynomial equation system with the help of S-tensors. 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 Lotka-Volterra 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.
  3. Ergodicity in planar slow-fast systems through slow relation functions
    (with R. Huzak and C. Kuehn)
  4. On Metzler positive systems on hypergraphs
    (with S. Cui, G. Zhang, and M. Cao)
  5. On network dynamical systems with a nilpotent singularity
    (with C. Kuehn)
  6. General SIS diffusion process with direct and indirect spreading on a hypergraph
    (with S. Cui, F. Liu, and M. Cao)
  7. Nonlinear Laplacian Dynamics: Symmetries, Perturbations, and Consensus
    (with R. Bonetto)
  8. The hyperbolic umbilic singularity in fast-slow systems
    (with C. Kuehn and M. Steinert)

Journals:

  1. On discrete-time polynomial dynamical systems on hypergraphs
    (with S. Cui, G. Zhang, and M. Cao)
    IEEE L-CSS, 2024
  2. Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling
    (with C. Kuehn and I. Longo)
    SIAM Journal of Applied Dynamical Systems
  3. Discrete-time Layered-network Epidemics Model with Time-varying Transition Rates and Multiple Resources
    (with S. Cui, F. Liu, and M. Cao)
    Automatica, 2024
  4. Stable Chimera States: A Geometric Singular Perturbation Approach
    (with L. Venegas and M. Cao)
    Chaos, 2023
  5. Simulation-based 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
  6. Slow-fast torus knots
    (with R. Huzak)
    Bull. Belgian Math. Soc., 2022.
  7. 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.
  8. Controlling canard cycles
    (with C. Kuehn)
    Journal of Dynamical and Control Systems, 2021.
  9. 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.
  10. Geometric analysis of Oscillations in the Frzilator model
    (with H. Tafgvafarad, P. Szmolyan and M. Cao)
    Journal of Mathematical Analysis and Applications, 2021.
  11. Extended and symmetric loss of stability for canards in planar fast-slow maps
    (with M. Engel)
    SIAM Journal on Applied Dynamical Systems, 2020.
  12. On Fast–Slow Consensus Networks with a Dynamic Weight
    (with C. Kuehn)
    Journal of Nonlinear Science, 2020.
  13. Stabilization of a class of slow-fast control systems at non-hyperbolic points 
    (with J. M. A. Scherpen, and D. del Puerto-Flores)
    Automatica, 2019.
  14. Improving the region of attraction of a non-hyperbolic point in slow-fast systems with one fast direction
    (with J. M. A. Scherpen)
    IEEE Control Systems Letters, 2018.
  15. Parameter-robustness analysis for a biochemical oscillator model describing the social-behavior transition phase of myxobacteria
    (with H. Tafgvafarad and M. Cao)
    Proceedings of the Royal Society A, 2018.
  16. Model order reduction and composite control for a class of slow-fast systems around a non-hyperbolic point
    (with J. M. A. Scherpen)
    IEEE Control Systems Letters, 2017.
  17. Limit sets within curves where trajectories converge to
    (with P. Ramazi and M. Cao)
    Applied Mathematics Letters, 2017.
  18. Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach
    (with J. Collado).
    Applied Mathematics, 2016.
  19. Analysis of a slow fast system near a cusp singularity
    (with H. W. Broer and R. Roussarie)
    Journal of Differential Equations, 2016.
  20. Formal normal form of Ak slow-fast systems 
    Comptes Rendus Mathematique, 2015.
  21. Bifurcations of a non-gravitational interaction problem
    (with X. Liu)
    Applied Mathematics and Computation, 2015.
  22. Polynomial normal forms of Constrained Differential Equations with three parameters
    (with H. W. Broer)
    Journal of Differential Equations, 2014.

Conference proceedings:

  1. Species Coexistence and Extinction Resulting from Higher-order Lotka-Volterra Two-Faction Competition
    (with S. Cui, Q. Zhao and M. Cao)
    62nd IEEE Conference on Decision and Control, 2023
  2. A topological perspective on singular canards for critical sets with transverse intersections
    (with R. Bonetto)
  3. A survey on the blow-up method for fast-slow systems ,
     (with C. Kuehn)
    Contemporary Mathematics, 2021, 775, pp. 115–160.
  4. Nonlinear adaptive stabilization of a class of planar slow-fast systems at a non-hyperbolic point
    (with J. M. A. Scherpen and D. del Puerto-Flores)
    American Control Conference 2017.
  5. Stabilization of a planar slow-fast system at a non-hyperbolic point
    (with J. M. A. Scherpen)
    Mathematical Theory of Networks and Systems 2016.
  6. Model order reduction of a flexible-joint robot: a port-Hamiltonian approach
     (with M. Munoz-Arias and J. M. A. Scherpen)
    IFAC Symposium on Nonlinear Control Systems 2016.
  7. Estabilización de Redes Complejas Fraccionarias de Sistemas de Lorenz y Sistemas de Chen
     (with R. Martínez-Martínez, J. A. León and G. Fernández-Anaya)
    Congreso de la Asociación de México de Control Automático, 2009.