zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Bifurcation analysis in an age-structured model of a single species living in two identical patches. (English) Zbl 1185.34101
Summary: We consider the age-structured model of a single species living in two identical patches derived in So et al. [J. W.-H. So, J. Wu and X. Zou, J. Math. Biol. 43, No.1, 37–51 (2001; Zbl 0986.92039)]. We chose a birth function that is frequently used but different from the one used in So et al. which leads to a different structure of the homogeneous equilibria. We investigate the stability of these equilibria and Hopf bifurcations by analyzing the distribution of the roots of associated characteristic equation. By the theory of normal form and center manifold, an explicit algorithm for determining the direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived. Finally, some numerical simulations are carried out for supporting the analytic results.
34K18Bifurcation theory of functional differential equations
37N25Dynamical systems in biology
92D25Population dynamics (general)
[1]Metz, J. A. J.; Diekmann, O.: J.a.j.metzo.diekmannthe dynamics of physiologically structured populations, The dynamics of physiologically structured populations (1986)
[2]Smith, H. L.: A structured population model and a related functional-differential equation: global attractors and uniform persistence, J. dyn. Diff. eq. 6, 71-99 (1994) · Zbl 0794.34061 · doi:10.1007/BF02219189
[3]So, J. W. -H.; Wu, J.; Zou, X.: Structured population on two patches: modeling dispersal and delay, J. math. Biol. 43, 37-51 (2001) · Zbl 0986.92039 · doi:10.1007/s002850100081
[4]Cooke, K.; Den Driessch, P. Van; Zou, X.: Interaction of maturation delay and nonlinear birth in population and epidemic models, J. math. Biol. 39, 332-352 (1999) · Zbl 0945.92016 · doi:10.1007/s002850050194
[5]Wei, J.; Zou, X.: Birfurcation analysis of a population model and the resulting sis epidemic model with delay, J. comput. Appl. math. 197, 169-187 (2006) · Zbl 1098.92055 · doi:10.1016/j.cam.2005.10.037
[6]Beretta, E.; Kuang, Y.: Geometric stability switch criteria in delay differential systems with delay dependant parameters, SIAM J. Math. anal. 33, 1144-1165 (2002) · Zbl 1013.92034 · doi:10.1137/S0036141000376086
[7]Hassard, B. D.; Kazarinoff, N. D.; Wan, Y. H.: Theory and applications of Hopf bifurcation, (1981)
[8]Hale, J.: Theory of functional differential equations, (1977)
[9]Wei, J.; Ruan, S.: Stability and bifurcation in a neural network model with two delays, Phys. D 130, 225-272 (1999) · Zbl 1066.34511 · doi:10.1016/S0167-2789(99)00009-3
[10]Qu, Y.; Wei, J.: Bifurcation analysis in a time-delay model for prey – predator growth with stage-structure, Nonlinear dyn. 49, 285-294 (2007) · Zbl 1176.92056 · doi:10.1007/s11071-006-9133-x