66 citations · 117 across the 13 of their papers we have counts for
15 papers
Markov Chains and Random Walks with Memory on Hypergraphs: A Tensor-Based Approach
Shaoxuan Cui, Lingfei Wang, Hildeberto Jardon-Kojakhmetov +2
Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified…
On Tensor-based Polynomial Hamiltonian Systems
Shaoxuan Cui, Guofeng Zhang, Hildeberto Jardon-Kojakhmetov +1
It is known that a linear system with a system matrix A constitutes a Hamiltonian system with a quadratic Hamiltonian if and only if A is a Hamiltonian matrix. This provides a stra…
Higher-order Laplacian dynamics on hypergraphs with cooperative and antagonistic interactions
Shaoxuan Cui, Chencheng Zhang, Bin Jiang +2
Laplacian dynamics on a signless graph characterize a class of linear interactions, where pairwise cooperative interactions between all agents lead to the convergence to a common s…
On discrete-time polynomial dynamical systems on hypergraphs
Shaoxuan Cui, Guofeng Zhang, Hildeberto Jardón-Kojakhmetov +1
This paper studies the stability of discrete-time polynomial dynamical systems on hypergraphs by utilizing the Perron-Frobenius theorem for nonnegative tensors with respect to the…
Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling
Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Iacopo P. Longo
We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The re…
Stable Chimera States: A Geometric Singular Perturbation Approach
Luis Guillermo Venegas-Pineda, Hildeberto Jardón-Kojakhmetov, Ming Cao
Over the past decades chimera states have attracted considerable attention given their unexpected symmetry-breaking spatio-temporal nature, simultaneously exhibiting synchronous an…
A geometric analysis of the SIRS epidemiological model on a homogeneous network
Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Andrea Pugliese +1
We study a fast-slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model,…
A geometric analysis of the SIR, SIRS and SIRWS epidemiological models
Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Andrea Pugliese +1
We study fast-slow versions of the SIR, SIRS, and SIRWS epidemiological models. The multiple time scale behavior is introduced to account for large differences between some of the…
Geometric analysis of Oscillations in the Frzilator model
Hadi Taghvafard, Hildeberto Jardon-Kojakhmetov, Peter Szmolyan +1
A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range of…
Extended and symmetric loss of stability for canards in planar fast-slow maps
Maximilian Engel, Hildeberto Jardón-Kojakhmetov
We study fast-slow maps obtained by discretization of planar fast-slow systems in continuous time. We focus on describing the so-called delayed loss of stability induced by the slo…
Controlling Canard Cycles
Hildeberto Jardon-Kojakhmetov, Christian Kuehn
Canard cycles are periodic orbits that appear as special solutions of fast-slow systems (or singularly perturbed Ordinary Differential Equations). It is well known that canard cycl…
On fast-slow consensus networks with a dynamic weight
Hildeberto Jardón-Kojakhmetov, Christian Kuehn
We study dynamic networks under an undirected consensus communication protocol and with one state-dependent weighted edge. We assume that the aforementioned dynamic edge can take v…
A survey on the blow-up method for fast-slow systems
Hildeberto Jardon-Kojakhmetov, Christian Kuehn
In this document we review a geometric technique, called \emph{the blow-up method}, as it has been used to analyze and understand the dynamics of fast-slow systems around non-hyper…
Stabilization of slow-fast systems at fold points
H. Jardon-Kojakhmetov, Jacquelien M. A. Scherpen, D. del Puerto-Flores
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of syst…
Analysis of a slow-fast system near a cusp singularity
H. Jardón-Kojakhmetov, Henk W. Broer, R. Roussarie
This paper studies a slow-fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two ma…