**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30855

##### Bifurcation Analysis of a Delayed Predator-prey Fishery Model with Prey Reserve in Frequency Domain

**Authors:**
Changjin Xu

**Abstract:**

In this paper, applying frequency domain approach, a delayed predator-prey ﬁshery model with prey reserve is investigated. By choosing the delay τ as a bifurcation parameter, It is found that Hopf bifurcation occurs as the bifurcation parameter τ passes a sequence of critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. The length of delay which preserves the stability of the positive equilibrium is calculated. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.

**Keywords:**
Stability,
Hopf Bifurcation,
frequency domain,
predator-prey model,
Nyquist criterion

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1081928

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