Applying a frequency domain approach, we investigate a phytoplankton model with time delay. We use the delay as a bifurcation parameter; as it passes through a sequence of critical values, Hopf bifurcation occurs. A family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations illustrate our theoretical results.
Submitted April 13, 2011. Published November 3, 2011.
Math Subject Classifications: 34K20.
Key Words: Phytoplankton model; Hopf bifurcation; stability; frequency domain; Nyquist criterion.
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| Changjin Xu |
Guizhou Key Laboratory of Economics System Simulation
School of Mathematics and Statistics
Guizhou College of Finance and Economics
Guiyang 550004, China
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