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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:
65P30Bifurcation problems (numerical analysis)
37C27Periodic orbits of vector fields and flows
35K55Nonlinear parabolic equations
35B32Bifurcation (PDE)
37K50Bifurcation problems (infinite-dimensional systems)