MatCont is a powerful toolbox for numerical bifurcation analysis focussing on smooth ODEs. A user can study equilibria, periodic and connecting orbits, and their stability and bifurcations. Here, we report on addition...
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We propose the use of exponential Runge-Kutta methods for the time integration of delay differential equations. The approach is based on their reformulation as abstract differential equations and the reduction of the ...
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We propose the use of exponential Runge-Kutta methods for the time integration of delay differential equations. The approach is based on their reformulation as abstract differential equations and the reduction of the latter to finite-dimensional systems of ordinary differential equations via pseudospectral discretization. We substantiate our results by means of some illustrative numerical simulations with EXPINT, a MATLAB package for exponential integrators.
In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility...
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In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases. c 2024 the Author(s), licensee AIMS Press.
We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, mod...
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We present a pragmatic approach to the sparse identification of nonlinear dynamics for systems with discrete delays. It relies on approximating the underlying delay model with a system of ordinary differential equatio...
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We present a pragmatic approach to the sparse identification of nonlinear dynamics for systems with discrete delays. It relies on approximating the underlying delay model with a system of ordinary differential equations via pseudospectral collocation. To minimize the reconstruction error, the new strategy avoids optimizing all possible multiple unknown delays, identifying only the maximum one. The computational burden is thus greatly reduced, improving the performance of recent implementations that work directly on the delay system.
Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects the regularity of the (coeffic...
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We propose a numerical method for computing the Lyapunov exponents of renewal equations (delay equations of Volterra type), consisting first in applying a discrete QR technique to the associated evolution family suita...
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In recent years we provided numerical methods based on pseudospectral collocation for computing the Floquet multipliers of different types of delay equations, with the goal of studying the stability of their periodic ...
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We propose a method for computing the Lyapunov exponents of renewal equations (delay equations of Volterra type) and of coupled systems of renewal and delay differential equations. The method consists of the reformula...
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