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math.DS2025
On an inverse tridiagonal eigenvalue problem and its application to synchronization of network motion
Luca Dieci, Cinzia Elia, Alessandro Pugliese
In this work, motivated by the study of stability of the synchronous orbit of a network with tridiagonal Laplacian matrix, we first solve an inverse eigenvalue problem which builds…
math.DS2025
Global bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients
Cinzia Elia, Roberta Fabbri, Carmen Núñez
Nonautonomous bifurcation theory is a growing branch of mathematics, for the insight it provides into radical changes in the global dynamics of realistic models for many real-world…
math.DS2024
Cusp bifurcations: numerical detection via two-parameter continuation and computer-assisted proofs of existence
Jean-Philippe Lessard, Alessandro Pugliese
This paper introduces a novel computer-assisted method for detecting and constructively proving the existence of cusp bifurcations in differential equations. The approach begins wi…