
Mathematical Biosciences and Engineering, 2019, 16(3): 15541574. doi: 10.3934/mbe.2019074.
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Optimal harvesting of a competitive nspecies stochastic model with delayed diffusions
1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China
2 Department of Mathematics, Swinburne University of Technology, Hawthorn, VIC 3122 Australia
Received: , Accepted: , Published:
Special Issues: Nonsmooth biological dynamical systems and applications
Keywords: stochastic delay model; optimal harvesting; stability in distribution; persistence in the mean
Citation: Fangfang Zhu, Xinzhu Meng, Tonghua Zhang. Optimal harvesting of a competitive nspecies stochastic model with delayed diffusions. Mathematical Biosciences and Engineering, 2019, 16(3): 15541574. doi: 10.3934/mbe.2019074
References:
 1. Z. Lu and Y. Takeuchi, Global asymptotic behavior in singlespecies discrete diffusion systems, J. Math. Biol., 32 (1993), 67–77.
 2. E. Beretta and Y. Takeuchi, Global stability of singlespecies diffusion Volterra models with continuous time delays, Bull. Math. Biol. 49 (1987), 431–448.
 3. D. Li, J. Cui and G. Song, Permanence and extinction for a singlespecies system with jump diffusion, J. Math. Anal. Appl., 430 (2015), 438–464.
 4. L. J. Allen, Persistence and extinction in singlespecies reactiondiffusion models, Bull. Math. Biol. 45.2 (1983), 209–227.
 5. W. Wang and T. Zhang, Caspase1Mediated Pyroptosis of the Predominance for Driving CD$_{4}$$^+$ T Cells Death: A Nonlocal Spatial Mathematical Model, B. Math. Biol., 80 (2018), 540582.
 6. Y. Cai andW.Wang, Fishhook bifurcation branch in a spatial heterogeneous epidemic model with crossdiffusion, Nonlinear Anal. Real World Appl., 30 (2016), 99–125.
 7. T. Zhang, X. Liu, X. Meng and T. Zhang, Spatiotemporal dynamics near the steady state of a planktonic system, Comput. Math. Appl., 75 (2018), 4490–4504.
 8. T. Zhang, T. Zhang, X. Meng, Stability analysis of a chemostat model with maintenance energy, Appl. Math. Lett., 68 (2017), 1–7.
 9. J. Zhou, C. Sang, X. Li, M. Fang and Z. Wang, H1 consensus for nonlinear stochastic multiagent systems with time delay, Appl. Math. Comput., 325 (2018), 41–58.
 10. K. Gopalsamy, Stability and oscillations in delay differential equations of population dynamics, Kluwer Academic, Dorecht. 1992.
 11. Y. Kuang, Delay differential equations with applications in population dynamics, Academic Press, 1993.
 12. X. Meng, F. Li and S. Gao, Global analysis and numerical simulations of a novel stochastic ecoepidemiological model with time delay, Appl. Math. Comput., 339 (2018), 701–726.
 13. T. Zhang, W. Ma and X. Meng, Global dynamics of a delayed chemostat model with harvest by impulsive flocculant input, Adv. Difference Equ., 2017 (2017), 115.
 14. G. Liu, X. Wang, X. Meng and S. Gao, Extinction and persistence in mean of a novel delay impulsive stochastic infected predatorprey system with jumps, Complexity, 2017 (2017), 15.
 15. Y. Tan, S. Tang, J. Yang and Z. Liu, Robust stability analysis of impulsive complexvalued neural networks with time delays and parameter uncertainties, J. Inequal. Appl., 2017 (2017), 215.
 16. T. Zhang and H. Zang, Delayinduced Turing instability in reactiondiffusion equations, Phys. Rev. E, 90 (2014) 052908.
 17. R. M. May, Stability and Complexity in Model Ecosystems, Princeton Univ. Press, NewYork, 2001.
 18. X. Yu, S. Yuan and T. Zhang, Survival and ergodicity of a stochastic phytoplanktonzooplankton model with toxin producing phytoplankton in an impulsive polluted environment, Appl. Math. Comput., 347 (2019), 249264.
 19. H. Qi, X. Leng, X. Meng and T. Zhang, Periodic Solution and Ergodic Stationary Distribution of SEIS Dynamical Systems with Active and Latent Patients, Qual. Theory Dyn. Syst., 18 (2019).
 20. S. Zhang, X. Meng, T. Feng and T. Zhang, Dynamics analysis and numerical simulations of a stochastic nonautonomous predatorprey system with impulsive effects, Nonlinear Anal. Hybrid Syst., 26 (2017), 19–37.
 21. M. Liu, H. Qiu and K. Wang, A remark on a stochastic predatorprey system with time delays, Appl. Math. Lett., 26 (2013), 318323.
 22. X. Meng and L. Zhang, Evolutionary dynamics in a LotkaVolterra competition model with impulsive periodic disturbance, Math. Method. Appl. Sci., 39 (2016), 177–188.
 23. L. Zhu and H. Hu, A stochastic SIR epidemic model with density dependent birth rate, Adv. Difference Equ., 2015 (2015), 1.
 24. X. Meng, S. Zhao, T. Feng and T. Zhang, Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis, J. Math. Anal. Appl., 433 (2016), 227–242.
 25. M. Liu and C. Bai, A remark on a stochastic logistic model with diffusion, Appl. Math. Lett., 228 (2014), 141–146.
 26. F. Bian, W. Zhao, Y. Song and R. Yue, Dynamical analysis of a class of preypredator model with BeddingtonDeangelis functional response, stochastic perturbation, and impulsive toxicant input, Complexity, 2017 (2017) Article ID 3742197.
 27. W. Wang, Y. Cai, J. Li and Z. Gui, Periodic behavior in a FIV model with seasonality as well as environment fluctuations, J. Franklin Inst., 354 (2017), 7410–7428.
 28. X. Song and L. Chen, Optimal harvesting and stability for a twospecies competitive system with stage structure, Math. Biosci., 170 (2001), 173–186.
 29. J. Liang, S. Tang and R. A. Cheke, Pure Btcrop and mixed seed sowing strategies for optimal economic profit in the face of pest resistance to pesticides and Btcorn, Appl. Math. Comput., 283 (2016), 6–21.
 30. S. Sharma and G. P. Samanta, Optimal harvesting of a two species competition model with imprecise biological parameters, Nonlinear Dynam., 77 (2014), 1101–1119.
 31. J. Xia, Z. Liu and R. Yuan, The effects of harvesting and time delay on predatorprey systems with Holling type II functional response, SIAM J. Appl. Math., 70 (2009), 1178–1200.
 32. W. Li, K. Wang, H. Su, Optimal harvesting policy for stochastic logistic population model, Appl. Math. Comput., 218 (2011), 157–162.
 33. X. Zou,W. Li and K.Wang, Ergodic method on optimal harvesting for a stochastic Gompertztype diffusion process, Appl. Math. Lett., 26 (2013), 170–174.
 34. Q. Song, R. H. Stockbridge and C. Zhu, On optimal harvesting problems in random environments, J. Soc. Ind. Appl. Math., 49 (2011), 859–889.
 35. G. Zeng, F. Wangand J. J. Nieto, Complexity of a delayed predatorprey model with impulsive harvesting and Holling type II functional response, Adv. Complex Syst., 11 (2008), 77–97.
 36. X. Zou, W. Li and K. Wang, Ergodic method on optimal harvesting for a stochastic Gompertztype diffusion process, Appl. Math. Lett., 26 (2013), 170–174.
 37. C. Ji, D. Jiang and N. Shi, Analysis of a predatorprey model with modified LeslieGower and Hollingtype II schemes with stochastic perturbation, J. Math. Anal. Appl., 359 (2009), 482–498.
 38. J. Bao and C. Yuan, Comparison theorem for stochastic differential delay equations with jumps, Acta Appl. Math., 116 (2011), 119.
 39. D. Jiang and N. Shi, A note on nonautonomous logistic equation with random perturbation, J. Math. Anal. Appl., 303 (2005), 164–172.
 40. D. Jiang, C. Ji, X. Li and D. O'Regan, Analysis of autonomous LotkaVolterra competition systems with random perturbation, J. Math. Anal. Appl., 390 (2012), 582–595.
 41. I. Barbalat, Systems d'equations differentielles d'osci d'oscillations nonlineaires, Rev. Roumaine Math. Pures Appl. 1959.
 42. X. Leng, T. Feng and X. Meng, Stochastic inequalities and applications to dynamics analysis of a novel SIVS epidemic model with jumps, J. Inequel. Appl., 2017 (2017), 138.
 43. J. Prato and J. Zabczyk, Ergodicity for infinite dimensional systems, Cambridge Univ. Press, Cambridge, (1996), 229.
 44. Y. Zhao, S. Yuan and I. Barbalat, Systems dequations differentielles doscillations nonlineaires, Phys. A., 477 (2017), 20–33.
 45. L. Liu and X. Meng, Optimal harvesting control and dynamics of two species stochastic model with delays, Adv. Differ Equat., 2017 (2017), 1–18.
 46. H. Qi, L. Liu and X. Meng, Dynamics of a nonautonomous stochastic SIS epidemic model with double epidemic hypothesis, Complexity, 2017 (2017), 14.
 47. D. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev., 43 (2001), 525–546.
 48. N. BrutiLiberati and E. Platen, Monte Carlo simulation for stochastic differential equations, Encyclopedia of Quantitative Finance, 10 (2010), 23–37.
 49. M. Liu and C. Bai, Optimal harvesting of a stochastic delay competitive model, Discrete Contin. Dyn. Syst. Ser. B., 22 (2017), 1493–1508.
 50. H. Ma and Y. Jia, Stability Analysis For Stochastic Differential EquationsWith Infinite Markovian Switchings, J. Math. Anal. Appl., 435 (2016), 593–605.
 51. M. Liu, X. He and J. Yu, Dynamics of a stochastic regimeswitching predatorprey model with harvesting and distributed delays, Nonlinear Anal. Hybrid Syst., 28 (2018), 87–104.
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