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Numerical steady state and Hopf bifurcation analysis on the diffusive Nicholson’s blowflies equation. (English) Zbl 1028.65138

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.

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

Citations:

Zbl 0923.35195
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References:

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