Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays

Changjin Xu, Maoxin Liao,  and Xiaofei He
  • 1 School of Mathematics and Statistics, Guizhou College of Finance and Economics, Luchongguan Rd 269, Guiyang 550004, PR China
  • 2 Faculty of Science, Hunan Institute of Engineering, Fuxing Rd 88, Xiangtan 411004, PR China
  • 3 School of Mathematics and Physics, Nanhua University, Changsheng Rd 26, Hengyang 421001, PR China
  • 4 Department of Mathematics, Zhangjiajie College of Jishou University, Renming Rd 120, Zhangjiajie 427000, PR China

Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays

In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also included.

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