TRACE-DDE: a Tool for Robust Analysis and Characteristic Equations for Delay Differential Equations. In the recent years the authors developed numerical schemes to detect the stability properties of different classes of systems involving delayed terms. The base of all methods is the use of pseudospectral differentiation techniques in order to get numerical approximations of the relevant characteristic eigenvalues. This chapter is aimed to present the freely available Matlab package TRACE-DDE devoted to the computation of characteristic roots and stability charts of linear autonomous systems of delay differential equations with discrete and distributed delays and to resume the main features of the underlying pseudospectral approach.

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  1. Pradhan, S.P.; Turi, J.: Effects of CPAP therapy on respiratory control system stability (2016)
  2. Sánchez Sanz, Julia; Getto, Philipp: Numerical bifurcation analysis of physiologically structured populations: consumer-resource, cannibalistic and trophic models (2016)
  3. Seuret, Alexandre; Gouaisbaut, Frédéric; Ariba, Yassine: Complete quadratic Lyapunov functionals for distributed delay systems (2015)
  4. Gumussoy, Suat; Gahinet, Pascal: Computer Aided Control System design for time delay systems using MATLAB$^\circledR$ (2014)
  5. Qiao, Wei; Sipahi, Rifat: Delay-dependent coupling for a multi-agent LTI consensus system with inter-agent delays (2014)
  6. Vyhlídal, Tomáš; Zítek, Pavel: QPmR-quasi-polynomial root-finder: algorithm update and examples (2014)
  7. Yi, Sun; Duan, Shiming; Nelson, Patrick W.; Ulsoy, A.Galip: Analysis and control of time delay systems using the LambertWDDE Toolbox (2014)
  8. Nakaoka, Shinji; Aihara, Kazuyuki: Stochastic simulation of structured skin cell population dynamics (2013)
  9. Qiao, Wei; Sipahi, Rifat: A linear time-invariant consensus dynamics with homogeneous delays: analytical study and synthesis of rightmost eigenvalues (2013)
  10. Breda, D.: On characteristic roots and stability charts of delay differential equations (2012)
  11. Wu, Zhen; Michiels, Wim: Reliably computing all characteristic roots of delay differential equations in a given right half plane using a spectral method (2012)
  12. Selimefendigil, F.; Sujith, R.I.; Polifke, W.: Identification of heat transfer dynamics for non-modal analysis of thermoacoustic stability (2011)
  13. Veltz, Romain; Faugeras, Olivier: Stability of the stationary solutions of neural field equations with propagation delays (2011)
  14. Jarlebring, Elias; Meerbergen, Karl; Michiels, Wim: A Krylov method for the delay eigenvalue problem (2010)
  15. Liu, Shengqiang; Beretta, Edoardo; Breda, Dimitri: Predator-prey model of Beddington-DeAngelis type with maturation and gestation delays (2010)
  16. Münz, Ulrich; Papachristodoulou, Antonis; Allgöwer, Frank: Delay robustness in consensus problems (2010)