![]() ![]() Huang, J., Gong, Y., Chen, J.: Multiple bifurcations in a predator–prey system of Holling and Leslie type with constant-yield prey harvesting. Hassard, B.D., Kazarinoff, N.D., Wan, Y.H.: Theory and Applications of Hopf Bifurcation. Gupta, R.P., Chandra, P.: Bifurcation analysis of modified Leslie–Gower predator–prey model with Michaelis-Menten type prey harvesting. ![]() Guin, L.N., Mandal, P.K.: Spatial pattern in a diffusive predator–prey model with sigmoid ratio-dependent functional response. Gourley, S.A., Kuang, Y.: A stage structured predator–prey model and its dependence on maturation delay and death rate. Gámez, M., Martínez, C.: Persistence and global stability in a predator–prey system with delay. Gakkhar, S., Singh, A.: Complex dynamics in a prey–predator system with multiple delays. 37(6), 4337–4349 (2013)ĭong, Q., Ma, W., Sun, M.: The asymptotic behavior of a chemostat model with Crowley–Martin type functional response and time delays. 231, 214–230 (2014)ĭevi, S.: Effects of prey refuge on a ratio-dependent predator–prey model with stage-structure of prey population. ![]() 58(1), 193–210 (1998)ĭeng, L., Wang, X., Peng, M.: Hopf bifurcation analysis for a ratio-dependent predator–prey system with two delays and stage structure for the predator. 8(3), 211–221 (1989)ĭai, G., Tang, M.: Coexistence region and global dynamics of a harvested predator–prey system. 73(3), 1307–1325 (2013)Ĭrowley, P.H., Martin, E.K.: Functional responses and interference within and between year classes of a dragonfly population. 59(3), 551–567 (1997)Ĭhakraborty, K., Haldar, S., Kar, T.K.: Global stability and bifurcation analysis of a delay induced prey–predator system with stage structure. Ecology 73(5), 1530–1535 (1992)īosch, F.V.D., Gabriel, W.: Cannibalism in an age-structured predator–prey system. Academic Press, New York (1963)īeretta, E., Kuang, Y.: Geometric stability switch criteria in delay differential systems with delay dependent parameters. 35(7), 3255–3267 (2011)īairagi, N., Jana, D.: Age-structured predator–prey model with habitat complexity: oscillations and control. 241(1), 109–119 (2006)īairagi, N., Jana, D.: On the stability and Hopf bifurcation of a delay-induced predator–prey system with habitat complexity. 52(3), 855–869 (1992)Īrino, J., Wang, L., Wolkowicz, G.S.K.: An alternative formulation for a delayed logistic equation. 101(2), 139–153 (1990)Īiello, W.G., Freedman, H.I., Wu, J.: Analysis of a model representing stage-structured population growth with state-dependent time delay. Finally, computer simulation and graphical illustrations have been carried out to support our theoretical investigations.Īiello, W.G., Freedman, H.I.: A time-delay model of single-species growth with stage structure. The direction and stability of Hopf-bifurcation are also studied by using normal form method and center manifold theorem. It changes the stability behavior of the system into instability, even with the switching of stability. Our model analysis shows that time delay plays a vital role in governing the dynamics of the system. Further, the existence of periodic solutions through Hopf-bifurcation is shown with respect to both the delays. Hopf-bifurcation with respect to different parameters has also been studied for the system. We analyzed the equilibrium points, local and global asymptotic behavior of interior equilibrium point for the non-delayed system. It is assumed that the immature prey population is consumed by predators with Holling type I functional response and the interaction between mature prey and predator species is followed by Crowley–Martin-type functional response. This study proposes a three-dimensional prey–predator model with stage structure in prey (immature and mature) including maturation delay in prey population and gestation delay in predator population. ![]()
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