Stability analysis of age-structured population equations by pseudospectral differencing methods

Journal of Mathematical Biology

Volumn 54, Issue 5, 2007, Pages 701-720

  Breda, Dimitri ^a   Cusulin, Caterina ^b   Iannelli, Mimmo ^b   Maset, Stefano ^c   Vermiglio, Rossana ^a  

^a UNIVERSITY OF UDINE   (Italy)

^b UNIVERSITY OF TRENTO   (Italy)

^c UNIVERSITY OF TRIESTE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

AGE; ARTICLE; BIOLOGICAL MODEL; HUMAN; MATHEMATICAL COMPUTING; POPULATION DYNAMICS; STATISTICAL MODEL;

AGE FACTORS; HUMANS; LINEAR MODELS; MODELS, BIOLOGICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; POPULATION DYNAMICS;

EID: 34248376901     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-006-0064-4     Document Type: Article

References (18)

1. Breda, D.: The infinitesimal generator approach for the computation of characteristic roots for delay differential equations using BDF methods. Research Report RR17/2002, Department of Mathematics and Computer Science, Università di Udine, Italy (2002)
2. Breda, D.: Numerical computation of characteristic roots for delay differential equations. Ph.D. Thesis, Department of Pure and Applied Mathematics, Università di Padova (2003)
3. Breda, D.: Methods for numerical computation of characteristic roots for delay differential equations: experimental comparison. Sci. Math. Jpn. 58(2), 377-388 (2003)
4. Breda, D.: Solution operator approximation for characteristic roots of delay differential equations. Appl. Numer. Math. 56, 305-31.7 (2006)
5. Breda, D., Maset, S., Vermiglio, R.: Computing the characteristic roots for delay differential equations. IMA J. Numer. Anal. 24(1), 1-19 (2004)
6. Breda, D., Maset, S., Vermiglio, R.: Pseudospectral differencing methods for characteristic roots of delay differential equations. SIAM J. Sci. Comput. 27(2), 482-495 (2005)
7. Con way, J.B.: Functions of One Complex Variable, GTM series no. 11,2nd edn. Springer, Berlin Heidelberg New York (1978)
8. Diekmann, Q., Montijn, R.: Prelude to Hopf bifurcation in an epidemic model: analysis of a characteristic equation associated with a nonlinear Volterra integral equation. J. Math. Biol. 14, 117-127 (1982)
9. Diekmann, O., van Gils, S.A., Verduyn Lunel, S.M., Walther, H.O.: Delay Equations-Functional, Complex and Nonlinear Analysis, AMS series no. 110. Springer, Berlin Heidelberg New York (1995)
10. Engelborghs, K., Roose, D: Numerical computation of stability and detection of Hopf bifurcations of steady-state solutions of delay differential equations. Adv. Comput. Math. 10(3-4), 271-289 (1999)
11. Engelborghs, K., Roose, D.: On stability of LMS methods and characteristic roots of delay differential equations. SIAM J. Numer. Anal. 40(2), 629-650 (2002)
12. Engelborghs, K., Luzyanina, T., Samaey, G: DDE-BIFTOOL v. 2.00: a Matlab package for bifurcation analysis of delay differential equations. Report TW330, Department of Computer Science, K. U. Leuven, Belgium (2001)
13. Engelborghs, K., Luzyanina, T., Roose, D.: Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL. ACM 'Irans. Math. Softw. 28(1), 1-21 (2002)
14. Iannelli, M.: Mathematical theory of age-structured population dynamics. In: Applied Mathematics Monographs (C.N.R.). Giardini Editori e Stampatori, Pisa, Italy (1994)
15. Luzyanina, T., Engelborghs, K., Roose, D.: Computing stability of differential equations with bounded distributed delays. Numer. Algorithms 34(1), 41-66 (2003)
16. Trefethen, L.N.: Spectral Methods in MATLAB. SIAM, Software-Environment- Tools series, Philadelphia (2000)
17. Trefethen, L.N., Trummer, M.R.: An instability phenomenon in spectral methods. SIAM J. Numer. Anal. 24(5), 1008-1023 (1987)
18. Webb, G.F.: Theory of Nonlinear Age-Dependent Population Dynamics. Marcel Dekker, New York (1985)