×

Dynamical analysis in a stochastic bioeconomic model with stage-structuring. (English) Zbl 1354.37100

Summary: This article studies a class of stage-structured bioeconomic models with stochastic fluctuations. The stochastic bioeconomic model is simplified to Itô equation by stochastic averaging method. The stochastic stability, Hopf bifurcation, D-bifurcation and P-bifurcation are discussed based on the system’s maximal Lyapunov exponent and dynamic systems invariant measure Lyapunov exponent. Numerical simulations are presented to illustrate our main results.

MSC:

37N40 Dynamical systems in optimization and economics
93D30 Lyapunov and storage functions
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Zhang, Y., Zhang, Q.L.: Dynamic behavior in a delayed stage-structured population model with stochastic fluctuation and harvesting. Nonlinear Dyn. 66, 231-245 (2011) · Zbl 1303.92109 · doi:10.1007/s11071-010-9923-z
[2] Zhang, X.A., Chen, L.S., Neumann, A.U.: The stage structured predator-prey model and optimal harvesting policy. Math. Biosci. 168, 201-210 (2000) · Zbl 0961.92037 · doi:10.1016/S0025-5564(00)00033-X
[3] Sun, C.J., Lin, Y.P., Han, M.A.: Dynamic analysis for a stage-structure competitive system with mature population harvesting. Chaos Solitons Fractals 31, 380-390 (2007) · Zbl 1145.34050 · doi:10.1016/j.chaos.2005.09.057
[4] Wang, J., Wang, K.: The optimal harvesting problems of a stage-structured population. Appl. Math. Comput. 148, 235-247 (2004) · Zbl 1037.92039 · doi:10.1016/j.amc.2003.07.019
[5] Nisbet, R.M., Gurney, W.S.C.: Modelling Fluctuating Populations. Wiley Interscience, New York (1982) · Zbl 0593.92013
[6] Saha, T., Bandyopadhyay, M.: Dynamical analysis of a delayed ratio-dependent prey-predator model within fluctuating environment. Appl. Math. Comput. 196, 458-478 (2008) · Zbl 1153.34051 · doi:10.1016/j.amc.2007.06.017
[7] Bandyopadhyay, M., Saha, T., Pal, R.: Deterministic and stochastic analysis of a delayed allelopathic phytoplankton model within fluctuating environment. Nonlinear Anal. 2, 958-970 (2008) · Zbl 1218.34098
[8] Kar, T.K.: Influence of environmental noises on the Gompertz model of two species fishery. Ecol. Model. 173, 283-293 (2004) · doi:10.1016/j.ecolmodel.2003.08.021
[9] Elsonbaty, A., Elsaid, A., Nour, H.M.: Effects of environmental fluctuation and time delay on ratio dependent hyperparasitism model. Commun. Nonlinear Sci. Numer. Simul. 16, 2609-2619 (2011) · Zbl 1221.34155
[10] Mukhopadhyay, B., Bhattacharyya, R.: Role of gestation delay in a plankton-fish model under stochastic fluctuations. Math. Biosci. 215, 26-34 (2008) · Zbl 1156.92043 · doi:10.1016/j.mbs.2008.05.007
[11] Huang, D.W., Wang, H.L., Feng, J.F., Zhu, Z.W.: Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics. Chaos Solitons Fractals 27, 1072-1079 (2006) · Zbl 1134.34312 · doi:10.1016/j.chaos.2005.04.086
[12] Huang, Z.T., Yang, Q.G., Cao, J.F.: Stochastic stability and bifurcation for the chronic state in Marchuks model with noise. Appl. Math. Model. 35, 5842-5855 (2011) · Zbl 1228.93086 · doi:10.1016/j.apm.2011.05.027
[13] Zhu, W.Q.: Nonlinear dynamics and control—Hamilton theoretical system frame. Science Press, Beijing (2003)
[14] Fang, W.X.: The research of stochastic stability and bifurcation of non-linear economical period model. Tianjin University doctoral dissertation (2007)
[15] Ericksona, R.A., Presley, S.M., Allen, L.J.S., Long, K.R., Cox, S.B.: A stage-structured, Aedes albopictus population model. Ecol. Model. 221, 1273-1283 (2010) · doi:10.1016/j.ecolmodel.2010.01.018
[16] Jiao, J.J., Long, W., Chen, L.S.: A single stage-structured population model with mature individuals in a polluted environment and pulse input of environmental toxin. Nonlinear Anal. 10, 3073-3081 (2009) · Zbl 1162.92330 · doi:10.1016/j.nonrwa.2008.10.007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.