Bifurcation analysis for a ratiodependent predatorprey system with multiple delays
Authors
Dingyang Lv
 Department of Mathematics, Hunan First Normal College, Changsha, 410205 Hunan, P. R. China.
Wen Zhang
 School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205 Hunan, P. R. China.
 School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P. R. China.
Yi Tang
 Department of Mathematics, Hunan First Normal College, Changsha, 410205 Hunan, P. R. China.
Abstract
In this paper, we consider a ratiodependent predatorprey system with multiple delays where the dynamics
are logistic with the carrying capacity proportional to prey population. By choosing the sum \(\tau\)
of two delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of
Hopf bifurcation are investigated. Furthermore, the direction of Hopf bifurcation and the stability of the
bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem
for functional differential equations. Finally, some numerical simulations are carried out for illustrating the
theoretical results.
Keywords
 Ratiodependent
 delay
 Hopf bifurcation
 center manifold
 periodic solutions.
MSC
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