Stability and bifurcation in a delayed predator–prey system with Beddington–DeAngelis functional response

By Zhihua Liu, Rong Yuan. 2004

75 citations recorded by the source corpus.

We consider a delayed predator–prey system with Beddington–DeAngelis functional response. The stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhaes. An example is given and numerical simulations are performed to illustrate the obtained results.

Subfields: Applied Mathematics, Genetics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/0d6f6f60b2e0ba3aa0c6714ea7547a82cee9898b

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In Applied Mathematics

1. Zhien Ma
2. Rui Xu
3. Yongli Song
4. Sanling Yuan

In Genetics

1. Sanling Yuan
2. Yongli Song
3. Sourav Kumar Sasmal

In Public Health, Environmental and Occupational Health

1. Sanling Yuan
2. Rui Xu
3. Zhien Ma
4. Yongli Song
5. Sourav Kumar Sasmal

Citations in the corpus

• Optimal harvesting and complex dynamics in a delayed eco-epidemiological model with weak Allee effects (2017, background): “The whole transformation process requires time, thus we have considered a constant time lag τ(> 0) for the gestation of predator (Freedman and Rao, 1983; Freedman et al., 1989; Wang and Ma, 1991; Gopalsamy, 1992; Kuang, 1993; Liu and Yuan, 2004; Chen et al., 2007; Xua et al., 2009).”
• RETRACTED: Stability and Hopf bifurcations in a delayed Leslie–Gower predator–prey system (2009, methodology): “We refer to the monographs of Cushing [8], Gopalsamy [9], Kuang [10] for general delayed biological systems and to Beretta and Kuang [11,12], Faria and Magalháes [13], Gopalsamy [14,15], May [16], Song and Wei [17], Xiao and Ruan [18], Liu and Yuan [19] and the references cited therein for studies o”
• Stability and bifurcation analysis on a ratio-dependent predator-prey model with time delay (2009, background): “The effect of time delay due to gestation of the predator on the dynamics of predator–prey models has been studied by a number of authors (see, for example, [15–17] and references cited therein).”
• Global stability of a nonlinear stochastic predator-prey system with Beddington-DeAngelis functional response (2011, unknown): “[9–20] and references therein.”