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Lande, R.: Risks of population extinction from demographic and envi- ronmental stochasticity and random catastrophes. Lambert, M.S., Control of Norway rats in the agricultural environment: alternatives to rodenticide use, (Thesis) (PhD). Krivan, V.: On the Gause predator–prey model with a refuge: A fresh look at the history. Kar, T.K.: Modelling and analysis of a harvested prey-predator system incorporating a prey refuge. Jana, S., Chakraborty, M., Chakraborty, K., Kar, T.K.: Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge. Jana, D.: Chaotic dynamics of a discrete predator-prey system with prey refuge. Iwasa, Y., Hakoyama, H., Nakamaru, M., Nakanishi, J.: Estimate of pop- ulation extinction risk and its application to ecological risk management. Holling, C.S.: The functional response of predators to prey density and its role in mimicry and Population regulation. Cambridge University Press, Cambridge (1981)
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Hassard, B.D., Kazarinoff, N.D., Wan, Y.H.: Theory and application of hopf bifurcation. Guan, X., Wang, W., Cai, Y.: Spatiotemporal dynamics of a Leslie-Gower predator–prey model incorporating a prey refuge. Gopalsamy, K., He, X.: Delay-independent stability in bidirectional asso- ciative memory networks. Gonzalez-Olivares, E., Gonzlez-Yanez, B., Becerra-Klix, R., Ramos- Jiliberto, R.: Multiple stable states in a model based on predator-induced defenses. Ghosh, J., Sahoo, B., Poria, S.: Prey-predator dynamics with prey refuge providing additional food to predator. Gause, G.F., Smaragdova, N.P., Witt, A.A.: Further studies of interaction between predators and prey. 207, 138–160 (2007)Ĭlark, M.E., Wolcott, T.G., Wolcott, D.L., Hines, A.H.: Intraspecific inter- ference among foraging blue crabs Callinectes sapidus: interactive effects of predator density and prey patch distribution. 218, 9271–9290 (2012)Ĭhen, C.C., Hsui, C.Y.: Fishery policy when considering the future opportunity of harvesting, Math. 42, 1474–1484 (2009)Ĭhakraborty, K., Jana, S., Kar, T.K.: Global dynamics and bifurcation in a stage structured prey predator fishery model with harvesting. Wiley (1982)Ĭelik, C.: Hopf bifurcation of a ratio-dependent predator–prey system with time delay. Kluwer Academic, Dordrecht, Netherlands (1996)īirkoff, G., Rota, G.C.: Ordinary differential equations, Ginn. Both mathematically and biologically, the study and conclusions of this work are intriguing.Īfanasev, V.N., Kolmanowski, V.B., Nosov, V.R.: Mathematical Theory of Control System Design. Numerical computations are often carried out in order to verify and visualise the various theoretical findings posed. Besides, environmental stochasticity of the white noise type has an impact on defining the contours of the scheme and the attendant estimates flowing therein. The governing equations associated with the direction as well as the stability of the bifurcating periodic solutions are determined through normal form theory and the centre manifold theorem. The moment the latency parameters move beyond the initial values, Hopf bifurcation occurs. The paper brings out in unambiguous terms the vital role of delay parameters, which show conditions wherein the coexistence equilibrium achieves stability and the values beyond which it reports instability. According to previous research, delay destabilises the mechanism in general, and equilibrium loss of stability occurs as a result of Hopf-bifurcation. We often suggest an updated Holling–Tanner prey–predator scheme in which the predator has a continuous time interval to allow for the predator's development cycle. The system's local stability was tested around a steady system near the biologically feasible equilibrium stage, and the model's global stability was assessed using the Lyapunov function. For instance, the system’s uniform boundedness is shown.
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In the absence of a host, prey develops logistically in this model. This study looked at the dynamics of a prey–predator mechanism with a Holling type II feature response that integrated prey refuge and the predator community with intra-specific rivalry.