
Mathematical Biosciences and Engineering, 2020, 17(4): 32403251. doi: 10.3934/mbe.2020184
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Extinction and stationary distribution of a competition system with distributed delays and higher order coupled noises
Department of Mathematics, Hubei Minzu University, Enshi, Hubei 445000, China
Received: , Accepted: , Published:
References
1. A. J. Lotka, Elements of Mathematical Biology, Dover, (1924), 167194.
2. V. Volterra, Leçons sur la théorie mathématique de la lutte pour la vie, Bull. Amer. Math. Soc., 42 (1936), 304305.
3. F. J. Ayala, M. E. Gilpin, J. G. Enrenfeld, Competition between species: theoretical models and experimental tests, Theoret. Population Biol., 4 (1973), 331356.
4. S. Ahmad, On the Nonautonomous VolterraLotka Competition Equations, Proc. Amer. Math. Soc., 117 (1993), 199204.
5. M. L. Zeeman, Extinction in competitive LotkaVolterra systems, Proc. Amer. Math. Soc., 123 (1995), 8796.
6. J. Y. Wang, Z. S. Feng, A nonautonomous competitive system with stage structure and distributed delays, Proc. Roy. Soc. Edinburgh Sect. A, 140 (2010), 10611080.
7. F. M. de Oca, L. Perez, Extinction in nonautonomous competitive LotkaVolterra systems with infinite delay, Nonlinear Anal., 75 (2012), 758768.
8. Z. Li, M. A. Han, F. D. Chen, Influence of feedback controls on an autonomous LotkaVolterra competitive system with infinite delays, Nonlinear Anal. Real World Appl., 14 (2013), 402413.
9. J. M. Cushing, Integrodifferential equations and delay models in population dynamics, in Lecture Notes in Biomathematics, Springer Science & Business Media, (2013).
10. N. Macdonald, Time Lags in Biological Models, in Lecture Notes in Biomathematics, Springer Science & Business Media, (2013).
11. X. H. Wang, H. H. Liu, C. L. Xu, Hopf bifurcations in a predatorprey system of population allelopathy with a discrete delay and a distributed delay, Nonlinear Dynam., 69 (2012), 21552167.
12. C. H. Zhang, X. P. Yan, G. H. Cui, Hopf bifurcations in a predatorprey system with a discrete delay and a distributed delay, Nonlinear Anal. Real World Appl., 11 (2010), 41414153.
13. Q. Liu, D. Q. Jiang, Stationary distribution and extinction of a stochastic predatorprey model with distributed delay, Appl. Math. Lett., 78 (2018), 7987.
14. W. J. Zuo, D. Q. Jiang, X. G. Sun, T. Hayat, A. Alsaedi, Longtime behaviors of a stochastic cooperative LotkaVolterra system with distributed delay, Phys. A, 506 (2018), 542559.
15. Q. L. Wang, Z. J. Liu, Z. X. Li, R. A. Cheke, Existence and global asymptotic stability of positive almost periodic solutions of a twospecies competitive system, Int. J. Biomath., 7 (2014), 1450040.
16. Q. Li, Z. J. Liu, S. L. Yuan, Crossdiffusion induced Turing instability for a competition model with saturation effect, Appl. Math. Comput., 347 (2019), 6477.
17. J. Hu, Z. J. Liu, Incorportating coupling noises into a nonlinear competitive system with saturation effect, Int. J. Biomath., 13 (2020), 2050012.
18. H. C. Chen, C. P. Ho, Persistence and global stability on competition system with timedelay, Tunghai Sci., 5 (2003), 7199.
19. Z. J. Liu, R. H. Tan, Y. P. Chen, Modeling and analysis of a delayed competitive system with impulsive perturbations, Rocky Mountain J. Math., 38 (2008), 15051523.
20. R. M. May, Stability and Complexity in Model Ecosystem, Princeton University Press, (2001).
21. X. Y. Li, X. R. Mao, Population dynamical behavior of nonautonomous LotkaVolterra competitive system with random perturbation, Discrete Contin. Dyn. Syst., 24 (2009), 523545.
22. F. Y. Wei, C. J. Wang, Survival analysis of a singlespecies population model with fluctuations and migrations between patches, Appl. Math. Model., 81 (2020), 113127.
23. A. Caruso, M. E. Gargano, D. Valenti, A. Fiasconaro, B. Spagnolo, Cyclic Fluctuations, Climatic Changes and Role of Noise in Planktonic Foraminifera in the Mediterranean Sea, Fluc. Noise Lett., 5 (2005), 349355.
24. A. Giuffrida, D. Valenti, G. Ziino, B. Spagnolo, A. Panebianco, A stochastic interspecific competition model to predict the behaviour of Listeria monocytogenes in the fermentation process of a traditional Sicilian salami, Eur. Food Res. Technol., 228 (2009), 767775.
25. D. Valenti, G. Denaro, A. La Cognata, B. Spagnolo, A. Bonanno, G. Basilone, et al., Picophytoplankton dynamics in noisy marine environment, Acta Phys. Pol., 43 (2012), 12271240.
26. Z. W. Cao, W. Feng, X. D. Wen, L. Zu, Stationary distribution of a stochastic predatorprey model with distributed delay and higher order perturbations, Phys. A, 521 (2019), 467475.
27. Q. Liu, D. Q. Jiang, T. Hayat, A. Alsaedi, Longtime behavior of a stochastic logistic equation with distributed delay and nonlinear perturbation, Phys. A, 508 (2018), 289304.
28. X. Q. Liu, S. M. Zhong, L. J. Xiang, Asymptotic properties of a stochastic predatorprey model with BeddingDeAngelis functional response, J. Appl. Math. Comput., 8 (2014), 171174.
29. X. R. Mao, Stochastic Differential Equations and their Applications, Horwood Publ, (1997).
30. A. Bahar, X. R. Mao, Stochastic delay LotkaVolterra model, J. Math. Anal. Appl., 292 (2004), 364380.
31. C. Lu, X. H. Ding, Persistence and extinction of a stochastic logistic model with delays and impulsive perturbation, Acta Math. Sci. Ser. B, 34 (2014), 15511570.
32. R Khasminskii, Stochastic Stability of Differential Equations, Springer Science & Business Media, (2011).
33. D. Y. Xu, Y. M. Huang, Z. G. Yang, Existence theorems for periodic Markov process and stochastic functional differential equations, Discrete Contin. Dyn. Syst., 24 (2009), 10051023.
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)