7 papers
Analysis of trophic networks: an optimisation approach
Jean-Guy Caputo, Valerie Girardin, Arnaud Knippel +3
We introduce a methodology to study the possible matter flows of an ecosystem defined by observational biomass data and realistic biological constraints. The flows belong to a poly…
Spectra of chains connected to complete graphs
J. -G. Caputo, G. Cruz-Pacheco, A. Knippel +1
We characterize the spectrum of the Laplacian of graphs composed of one or two finite or infinite chains connected to a complete graph. We show the existence of localized eigenvect…
Epidemic model on a network: analysis and applications to COVID-19
F. Bustamante-Castaneda, J. -G. Caputo, G. Cruz-Pacheco +2
We analyze an epidemic model on a network consisting of susceptible-infected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic…
Liouville type theorems, a priori estimates and existence of solutions for critical order Hardy-Hénon equations in
Wenxiong Chen, Wei Dai, Guolin Qin
In this paper, we consider the critical order Hardy-Hénon equations \begin{equation*} (-Δ)^{\frac{n}{2}}u(x)=\frac{u^{p}(x)}{|x|^{a}}, \,\,\,\,\,\,\,\,\,\,\, x \, \in \,\, \mathbb{…
On graph Laplacian eigenvectors with components in {-1,0,1}
J-G. Caputo, I. Khames, A. Knippel
We characterize all graphs for which there are eigenvectors of the graph Laplacian having all their components in {-1,+1} or {-1,0,+ 1}. Graphs having eigenvectors with components…
Localized solutions of nonlinear network wave equations
J. G. Caputo, I. Khames, A. Knippel +1
We study localized solutions for the nonlinear graph wave equation on finite arbitrary networks. Assuming a large amplitude localized initial condition on one node of the graph, we…