So, Joseph W.-H.; Wu, Jianhong; Yang, Yuanjie Numerical steady state and Hopf bifurcation analysis on the diffusive Nicholson’s blowflies equation. (English) Zbl 1028.65138 Appl. Math. Comput. 111, No. 1, 33-51 (2000). Summary: For the Dirichlet boundary value problem of the diffusive Nicholson’s blowflies equation, it was shown by J. W.-H. So and Y. Yang [J. Differ. Equations 150, No. 2, 317-348 (1998; Zbl 0923.35195)] that in a certain range of the parameter space, there is a unique positive steady state solution. In this paper, we propose a scheme to compute this steady state numerically. In addition, we describe an iterative procedure to locate the critical values of the delay where a Hopf bifurcation of time periodic solutions takes place near the steady state. Some numerical simulations of both schemes are given. Cited in 89 Documents MSC: 65P30 Numerical bifurcation problems 37C27 Periodic orbits of vector fields and flows 35K55 Nonlinear parabolic equations 35B32 Bifurcations in context of PDEs 37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems Keywords:numerical examples; Dirichlet boundary value problem; diffusive Nicholson’s blowflies equation; positive steady state solution; Hopf bifurcation; time periodic solutions Citations:Zbl 0923.35195 PDFBibTeX XMLCite \textit{J. W. H. So} et al., Appl. Math. Comput. 111, No. 1, 33--51 (2000; Zbl 1028.65138) Full Text: DOI References: [1] G. Adomian, Solving Frontier problems of physics. The Decomposition Method, Kluwer, Boston, 1994; G. Adomian, Solving Frontier problems of physics. The Decomposition Method, Kluwer, Boston, 1994 · Zbl 0802.65122 [2] Adomian, G., A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135, 501-544 (1988) · Zbl 0671.34053 [3] Adomian, G., A new approach to nonlinear partial differential equations, J. Math. Anal. Appl., 102, 420-434 (1984) · Zbl 0554.60065 [4] Rach, R., A convenient computational form for the Adomian polynomials, J. Math. Anal. Appl., 102, 415-419 (1984) · Zbl 0552.60061 [5] Seng, V.; Abbaoui, K.; Cherruault, Y., Adomian’s polynomials for nonlinear operators, Mathl. Comput. Modelling., 24, 59-65 (1996) · Zbl 0855.47041 [6] Abbaoui, K.; Cherruault, Y., Convergence of Adomian’s method applied to differential equations, Comput. Math. Appl., 102, 77-86 (1999) · Zbl 0938.93023 [7] Wazwaz, A. M., The decomposition method for approximate solution of the Goursat problem, Appl. Math. Comput., 69, 299-311 (1995) · Zbl 0826.65077 [8] A.M. Wazwaz, A First Course in Integral Equations, WSPC, New Jersey, 1997; A.M. Wazwaz, A First Course in Integral Equations, WSPC, New Jersey, 1997 · Zbl 0924.45001 [9] Wazwaz, A. M., A study on a boundary-layer equation arising in an incompressible fluid, Appl. Math. Comput., 87, 199-204 (1997) · Zbl 0904.76067 [10] L. Debnath, Nonlinear Partial Differential Equations, Birkhauser, Boston, 1997; L. Debnath, Nonlinear Partial Differential Equations, Birkhauser, Boston, 1997 · Zbl 0892.35001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.