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Articles

Optimal harvesting for a stochastic logistic model with S-type distributed time delay

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Pages 618-632 | Received 16 Jun 2016, Accepted 28 Nov 2016, Published online: 29 Dec 2016

References

  • J.H. Bao, Z.T. Hou, and C.G. Yuan, Stability in distribution of neutral stochastic differential delay equations with Markovian switching, Stat. Probab. Lett. 79 (2009), pp. 1663–1673.
  • J.H. Bao and C.G. Yuan, Comparison theorem for stochastic differential delay equations with jumps, Acta Appl. Math. 116 (2011), pp. 119–132.
  • I. Barbalat, Systems dequations differentielles d’osci d’oscillations [Systems d’equations differentielles d’oscillations nonlinearies], Rev. Roumaine Math. Pures Appl. 4 (1959), pp. 267–270.
  • J.R. Beddington and R.M. May, Harvesting natural populations in a randomly fluctuating environment, Science. 197 (1977), pp. 463–465.
  • C.W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewal Resources, Wiley, New York, 1976.
  • C.W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewal Resources, 2nd ed., Wiley, New York, 1990.
  • G. Da Prato and J. Zabczyk, Ergodicity for Infinite Dimensional Systems, Cambridge University Press, Cambridge, 1996.
  • T.C. Gard, Stability for multispecies population models in random environments, Nonlinear Anal. 10 (1986), pp. 1411–1419.
  • X.Y. Li and X.R. Mao, Population dynamical behavior of non-autonomous Lotka--Volterra competitive system with random perturbation, Discrete Contin. Dyn. Syst. 24 (2009), pp. 523–545.
  • M. Liu, Optimal harvesting policy of a stochastic predator-prey model with time delay, Appl. Math. Lett. 48 (2015), pp. 102–108.
  • M. Liu and C.Z. Bai, Optimal harvesting policy of a stochastic food chain population model, Appl. Math. Comput. 245 (2014), pp. 265–270.
  • M. Liu and C.Z. Bai, Optimal harvesting of a stochastic logistic model with time delay, J. Nonlinear Sci. 25 (2015), pp. 277–289.
  • M. Liu and C.Z. Bai, Analysis of a stochastic tri-trophic food-chain model with harvesting, J. Math. Biol. 73 (2016), pp. 597–625. doi:10.1007/s00285-016-0970-z.
  • M. Liu and C.Z. Bai, Optimal harvesting of a stochastic mutualism model with Lévy jumps, Appl. Math. Comput. 276 (2016), pp. 301–309.
  • M. Liu and K. Wang, Stochastic Lotka--Volterra systems with Lévy noise, J. Math. Anal. Appl. 410 (2014), pp. 750–763.
  • W.X. Li and K. Wang, Optimal harvesting policy for general stochastic logistic population model, J. Math. Anal. Appl. 368 (2010), pp. 420–428.
  • W.X. Li, K. Wang, and H. Su, Optimal harvesting policy for stochastic logistic population model, Appl. Math. Comput. 218 (2011), pp. 157–162.
  • X.R. Mao, Exponential Stability of Stochastic Differential Equations, Marcal Dekker, New York, 1994.
  • X.R. Mao, Stochastic stabilization and destabilization, Syst. Control Lett. 23 (1994), pp. 279–290.
  • X.R. Mao, Stochastic Differential Equations and Applications, Horwood Publishing Limited, England, 2007.
  • X.R. Mao, G. Marion, and E. Renshaw, Environmental Brownian noise suppresses explosions in population dynamics, Stoch. Process. Appl. 97 (2002), pp. 95–110.
  • L.S. Wang and D.Y. Xu, Global asymptotic stability of bidirectional associative memory neural networks with S-type distributed delays, Int. J. Syst. Sci. 33 (2002), pp. 869–877.
  • L.S. Wang, R.J. Zhang, and Y.F. Wang, Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays, Nonlinear Anal. 10 (2009), pp. 1101–1113.
  • F.Y. Wei and K. Wang, The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay, J. Math. Anal. Appl. 331 (2007), pp. 516–531.
  • X.H. Zhang, W.X. Li, M. Liu, and K. Wang, Dynamics of a stochastic Holling II one-predator two-prey system with jumps, Physica A 421 (2015), pp. 571–582.
  • C. Zhu and G. Yin, On hybrid competitive Lotka--Volterra ecosystems, Nonlinear Anal. 71 (2009), pp. e1370–e1379.
  • X.L. Zou and K. Wang, Optimal harvesting for a stochastic regime-switching logistic diffusion system with jumps, Nonlinear Anal. 13 (2014), pp. 32–44.

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