Author: Michela Palermo
MATLAB codes developed as part of Michela’s MSc thesis.
JL
tests the Johnson–Lindenstrauss random projection in finite dimension.JL_inf_Leg
randomly maps the first n normalised Legendre polynomials from \(L^2([0,1],\mathbb{R})\) to finite dimension, preserving their distances but for a certain relative error, with a certain probability.Comp_JL_F_Leg
compares the Johnson–Lindenstrauss random projection and the Fourier–Legendre projection from \(L^2([0,1],\mathbb{R})\) to finite dimension applied to the set of the first n normalised Legendre polynomials.Author: Cristian Tanase
A MATLAB code for computing the eigenvalues of the monodromy operator of the linearization around a periodic solution of a specific state-dependent DDE. The code was developed as part of Cristian’s MSc thesis.
Implementation of exponential Runge–Kutta methods for delay equations as described in [1] and demo examples of MATLAB scripts.
Author: Simone De Reggi
Package for the numerical approximation of the reproduction numbers of linear age-structured population models formulated as integro-partial differential equations with non-local boundary conditions according to the method of [2].
Author: Davide Liessi
Approximation via discrete QR method of the Lyapunov exponents of renewal equations and systems of coulped renewal and delay differential equations via pseudospectral discretization as ODEs (see [3]).
Author: Dimitri Breda
Codici MATLAB/Octave per il laboratorio “Dalla bisezione ai frattali di Newton” del Seminario Nazionale dei Licei Matematici in collaborazione con Paolo Giangrandi, Antonella Mereu, Chiara Milan e Marzia Toso dell’ISIS “A. Malignani” di Udine.
Author: Simone De Reggi
Package for the numerical approximation of the spectrum of the reformulation in terms of the integrated age-state of the infinitesimal generator associated to linear age-structured population models with nonlocal diffusion formulated as integro-partial differential equations (see [4]).
Author: Enrico Santi
Extension of MatCont implementing the methods [5] for delay differential equations and [6] for renewal equations and enabling their use via the GUI (see below for using the methods via the command line interface: DDEs, REs). The extension, based on version 7p4 of MatCont, was developed as part of Enrico’s BSc internship at CDLab. His BSc thesis contains the description of the changes and usage details.
Download (version of 29/01/2024; obsolete, see below)
Starting from version 7p5, the pseudospectral collocation method for delay equations is included in MatCont as the Delay Equation Importer. You can download MatCont from its SourceForge page. This version is kept here for documentation purposes only and no support will be given on it.
Slides for the talks presented at IFAC TDS 2022 in Montréal:
See the dedicated page.
Author: Simone De Reggi
Pseudospectral discretization of the reformulation in terms of the integrated states of the infinitesimal generator for population models with one and two physiological structures formulated as first-order hyperbolic PDEs (see [7]).
Author: Dimitri Breda
Software for simulating a model of honey bee health (see [8]).
Download from Zenodo, DOI: 10.5281/zenodo.7050516
Author: Simone De Reggi
Approximation of the basic reproduction number \(R_0\) in population models with two internal structures formulated as PDEs (see [9]).
Author: Dimitri Breda
Approximation of the basic reproduction number \(R_0\) for some population models with one internal structure formulated as PDEs (see [10] and [11]).
Author: Davide Liessi
MATLAB code extending the methods of eigTMN and eigTMNc to approximate the multipliers of linear coupled renewal equations and retarded functional differential equations with a piecewise approach (see [12] and [13]).
Author: Francesca Scarabel
MATLAB codes for the numerical bifurcation analysis of the ODE approximating system obtained by pseudospectral discretization of renewal equations with finite delay using the formulation for the integrated state (main reference [14]). The bifurcation analysis of the ODE system is performed using MatCont.
Author: Francesca Scarabel
MATLAB codes for the numerical bifurcation analysis of the ODE approximating system obtained by pseudospectral discretization of delay differential equations and renewal equations with finite delay (main reference [15]), using MatCont. The codes are organized in several folders corresponding to each publication.
Author: Francesca Scarabel
MATLAB codes for the numerical bifurcation analysis of the ODE approximating system obtained by pseudospectral discretization of structured population models formulated as PDE [16], using MatCont.
Author: Alessia Andò
Demo examples of Python scripts implementing the continuation of periodic solutions for models defined by renewal equations or systems of coupled renewal and delay differential equations, as described in [17].
Author: Alessia Andò
Demo examples of Python scripts implementing the internal continuation method described in [18].
See the dedicated page.
Author: Ilaria Fontana
MATLAB codes for discretizing equations with infinite delay via pseudospectral collocation and studying their bifurcations via continuation with MatCont. The codes were developed as part of Ilaria’s MSc thesis.
Author: Marco Gambone
MATLAB codes based on ADiMat [19] computing equilibria of epidemiological models and studying their stability. The codes were developed as part of Marco’s BSc thesis.
Author: Francesco Florian
C++ library providing interpolatory quadrature and differentiation weights. The library was developed as part of Francesco’s MSc thesis.
Authors: Davide Liessi and Dimitri Breda
MATLAB code extending the method of eigTMN to approximate the multipliers of linear coupled renewal equations and retarded functional differential equations. See [20] for renewal equations and [21] for coupled equations.
Authors: Dimitri Breda and Sara Della Schiava
MATLAB codes from a recent work inspired by Sara’s MSc thesis, see [22]. Based on the pseudospectral reduction to ODEs, with these codes one can approximate a number of Lyapunov exponents of a DDE. This version is tuned for the Mackey–Glass equation, but modification should be straightforward.
Authors: Dimitri Breda, Stefano Maset, and Rossana Vermiglio
MATLAB codes accompanying the recent book [23]. They are devoted to the computation of either the characteristic roots or multipliers of linear, respectively autonomous and periodic, delay differential equations. Chapter 8 of the book should be enough to learn and experimenting.
Authors: Dimitri Breda, Stefano Maset, and Rossana Vermiglio
A MATLAB package for the computation of level curves of surfaces. It is a grid-like approach based on adaptive triangulation. The method is described in [24]. The package contains a brief manual and test cases.
Authors: Dimitri Breda, Stefano Maset, and Rossana Vermiglio
A MATLAB GUI for computing characteristic roots and stability charts of linear autonomous systems of DDEs with several discrete and/or distributed delays, see the book chapter [25]. The GUI structure, developed at UniUD by Daniele Sechi in his BSc thesis, properly works on Mac OS X 10.3 (or superior) with MATLAB 7x, but is no longer maintained.