nach oben

nächster Artikel Dynamical analysis of a Lotka–Volterra competit...

Tipp

Dynamics of an impulsive diffusive ecological model with distributed delay and additive Allee effect

Zeitschrift:: Journal of Applied Mathematics and Computing > Ausgabe 1-2/2015

Autoren:: Liu Yang, Shouming Zhong

Abstract

In this paper, we proposed and investigated a model on the process of periodic harvesting and diffusion at different fixed moments using an impulsive differential equation with distributed delay and additive Allee effect. In this model, prey species was restricted to a single patch, and predator species will diffuse between two patches. By using the theories of impulsive equations, small amplitude perturbation skills and comparison techniques, we obtained the sufficient conditions ensuring the global asymptotical stability of the prey-eradication periodic solution and permanence of the system. Finally, some numerical simulations are carried out to consolidate the analytical findings.

Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten

Jetzt einloggen Kostenlos registrieren

Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 69.000 Bücher
über 500 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Umwelt
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 58.000 Bücher
über 300 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 50.000 Bücher
über 380 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Umwelt
Maschinenbau + Werkstoffe

Testen Sie jetzt 30 Tage kostenlos.

Jetzt informieren

Cui, J., Takeuchi, Y., Lin, Z.: Permanence and extinction for dispersal population systems. J. Math. Anal. Appl. 298, 73–93 (2004) CrossRefMATHMathSciNet

Xu, R., Ma, Z.E.: The effect of dispersal on the permanence of a predator-prey system with time delay. Nonlinear Anal. RWA 9, 354–369 (2008) CrossRefMATHMathSciNet

Cui, J., Chen, L.S.: Permanence and extinction in logistic and Lotka-Volterra systems with diffusion. J. Math. Anal. Appl. 258, 512–535 (2001) CrossRefMATHMathSciNet

Zhou, X.Y., Shi, X.Y., Song, X.Y.: Analysis of nonautonomous predator-prey model with nonlinear diffusion and time delay. Appl. Math. Comput. 196, 129–136 (2008) CrossRefMATHMathSciNet

Ding, W., Han, M.A.: Dynamic of a non-autonomous predator-prey system with infinite delay and diffusion. Comput. Math. Appl. 56, 1335–1350 (2008) CrossRefMATHMathSciNet

Chen, S., Zhang, J., Yong, T.: Existence of positive periodic solution for nonautonomous predator-prey system with diffusion and time delay. J. Comput. Appl. Math. 159, 375–386 (2003) CrossRefMATHMathSciNet

Song, X.Y., Chen, L.S.: Persistence and global stability for nonautonomous predator-prey systems with diffusion and time delays. Comput. Math. Appl. 35, 33–40 (1998) CrossRefMATHMathSciNet

Xu, R., Chaplain, M., Davidson, F.A.: Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays. Appl. Math. Comput. 148, 537–560 (2004) CrossRefMATHMathSciNet

Shao, Y.F.: Analysis of a delayed predator-prey system with impulsive diffusion between two patches. Math. Comput. Model. 52, 120–127 (2010) CrossRefMATH

10.

Jiao, J.J., Cai, S.H., Chen, L.S.: Dynamical analysis of a three-dimensional predator-prey model with impulsive harvesting and diffusion. Int. J. Bifurc. Chaos 21, 453–465 (2011) CrossRefMATHMathSciNet

11.

Jiao, J.J., Cai, S.H.: A delayed chemostat model with impulsive diffusion and input on nutrients. Adv. Diff. Equ. 2009 (2010). doi: 10.1155/2009/514240

12.

Jiao, J.J., Ye, K.L., Chen, L.S.: Dynamical analysis of a five-dimensioned chemostat model with impulsive diffusion and pulse input environmental toxicant. Chaos, Solitons, Fractals 44, 17–27 (2011) CrossRefMATHMathSciNet

13.

Jiao, J.J., Cai, S.H., Chen, L.S.: Dynamical behaviors of a delayed chemostat model with impulsive diffusion on nutrients. J. Appl. Math. Comput. 35, 443–457 (2011) CrossRefMATHMathSciNet

14.

Hui, J., Chen, L.S.: A single species model with impulsive diffusion. Acta Math. Appl. Sinica 21, 43–48 (2005) CrossRefMATHMathSciNet

15.

Wan, H.Y., Zhang, L., Li, H.L.: A single species model with symmetric bidirectional impulsive diffusion and dispersal delay. Appl. Math. 3, 1079–1088 (2012) CrossRef

16.

Wang, L., Liu, Z.J., Jing, H., Chen, L.S.: Impulsive diffusion in single species model. Chaos Solit. Fract. 33, 1213–1219 (2007) CrossRefMATH

17.

Dong, L.Z., Chen, L.S., Sun, L.H.: Optimal harvesting policy for inshore-offshore fishery model with impulsive diffusion. Acta. Math. Sci. 27, 405–412 (2007) CrossRefMATHMathSciNet

18.

Zhang, L., Teng, Z.D., DeAngelis, D.L., Ruan, S.G.: Single species models with logistic growth and dissymmetric impulse dispersal. Math. Biosci. 241, 188–197 (2013) CrossRefMATHMathSciNet

19.

Zhao, Z., Zhang, X.Q., Chen, L.S.: The effect of pulsed harvesting policy on the inshore-offshore fishery model with the impulsive diffusion. Nonlinear Dyn. 63, 537–545 (2011)

20.

Morozov, A., Petrovskii, S., Li, B.L.: Bifurcations and chaos in a predator-prey system with the Allee effect. Proc. Roy. Soc. Lond. B 271, 1407–1414 (2004) CrossRef

21.

Boukal, D.S., Sabelis, M.W., Berec, L.: How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses. Theor. Popul. Biol. 72, 136–147 (2007) CrossRefMATH

22.

Gascoigne, J.C., Lipcius, R.N.: Allee effects driven by predation. J. Appl. Ecol. 41, 801–810 (2004) CrossRef

23.

Kent, A., Patrick Doncaster, C., Sluckin, T.: Consequences for predators of rescue and Allee effects on prey. Ecol. Model. 162, 233–245 (2003) CrossRef

24.

Allee, W.C.: Animal aggregations, a study in general sociology. University of Chicago Press, Chicago (1931) CrossRef

25.

Stephens, P.A., Sutherland, W.J.: Consequences of the Allee effect for behaviour, ecology and conservation. Trends Ecol. 14, 401–405 (1999) CrossRef

26.

Kramer, A.M., Dennis, B., Liebhold, A.M., Drake, J.M.: The evidence for Allee effects. Popul. Ecol. 51, 341–354 (2009) CrossRef

27.

Aguirre, P., González-Olivares, E., Sáez, E.: Two limit cycles in a Leslie-Gower predator-prey model with additive Allee effect. Nonlinear Anal. RWA 10, 1401–1416 (2009) CrossRefMATH

28.

Aguirre, P., González-Olivares, E., Sáez, E.: Three limit cycles in a Leslie-Gower predator-prey model with additive Allee effect. SIAM J. Appl. Math. 69, 1244–1269 (2009) CrossRefMATHMathSciNet

29.

Berec, L., Angulo, E., Courchamp, F.: Multiple Allee effects and population management. Trends Ecol. Evol. 22, 185–191 (2007) CrossRef

30.

Conway, E.D., Smoller, J.A.: Global analysis of a system of predator-prey equations. SIAM J. Appl. Math. 46(4), 630–642 (1986) CrossRefMATHMathSciNet

31.

Bazykin, A.D.: Nonlinear Dynamics of Interacting Populations. World Scientific, Singapore (1998)

32.

Clark, C.W.: Mathematical Bioeconomics: The Optimal Management of Renewable Resources, 2nd edn. Wiley, New York (1990) MATH

33.

Clark, C.W.: The Worldwide Crisis in Fisheries: Economic Model and Human Behavior. Cambridge University Press, Cambridge (2007) CrossRef

34.

Courchamp, F., Clutton-Brock, T., Grenfell, B.: Inverse density dependence and the Allee effect. Trends Ecol. Evol. 14(10), 405–410 (1999) CrossRef

35.

Stephens, P.A., Sutherland, W.J.: Consequences of the Allee effect for behaviour, ecology and conservation. Trends Ecol. Evol. 14(10), 401–405 (1999) CrossRef

36.

Pei, Y., Liu, S., Liu, C., Chen, L.: The dynamics of an impulsive delay SI model with variable coefficients. Appl. Math. Model. 33, 2766–2776 (2009) CrossRefMATHMathSciNet

37.

Georgescu, P., Zhang, H., Chen, L.S.: Bifurcation of nontrivial periodic solution for an impulsively controlled pest management model. Appl. Math. Comput. 202, 675–687 (2008) CrossRefMATHMathSciNet

38.

Jiao, J.J., Chen, L.S.: A pest management SI model with biological and chemical control concern. Appl. Math. Comput. 196, 1018C1026 (2006)

39.

Li, Z.Q., Wang, W.M., Wang, H.L.: The dynamics of a Beddington-type system with impulsive control strategy. Chaos Solit. Fract. 29, 1229C1239 (2006)

40.

Yu, H.G., Zhong, S.M., Agarwal, R.P.: Mathematics analysis and chaos in an ecological model with an impulsive control strategy. Commun. Nonlinear Sci. Numer. Simul. 16, 776–786 (2011) CrossRefMATHMathSciNet

41.

Yu, H.G., Zhong, S.M., Ye, M.: Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay. Math. Comput. Simul. 80, 619–632 (2009) CrossRefMATHMathSciNet

42.

Lakshmikantham, V., Bainov, D.D., Simeonov, P.C.: Theory of Impulsive Differential. World Scientific, Singapore (1989) CrossRefMATH

43.

Bainov, D.D., Simeonnov, P.S.: System with Impulsive Effect: Stability Theory. Wiley, New York (1989)

44.

Bainov, D.D., Simeonov, P.S.: Impulsive Differential Equations: Asymptotic. World Scientific, Singapore (1993)

45.

Smith, H.L.: Cooperative systems of differential equations with concave nonlinearities. Nonlinear Anal. TMA 10, 1037–1052 (1986) CrossRefMATH

Titel: Dynamics of an impulsive diffusive ecological model with distributed delay and additive Allee effect
Autoren:: Liu Yang
Shouming Zhong
Publikationsdatum: 01.06.2015
DOI: https://doi.org/10.1007/s12190-014-0788-z
Verlag: Springer Berlin Heidelberg
Zeitschrift: Journal of Applied Mathematics and Computing
Ausgabe 1-2/2015
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085

Premium Partner

Bildnachweise

Springer Professional

Tipp

Weitere Artikel dieser Ausgabe durch Wischen aufrufen

Abstract

Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten

Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1-2/2015

Anti-periodic mild solutions to semilinear fractional differential equations

Existence result for nonlinear fractional differential equation with -Laplacian operator at resonance

The existence of solutions for boundary value problems of two types fractional perturbation differential equations

Empirical likelihood for composite quantile regression modeling

Minimal cyclic codes of length over , where is prime power of the form

An efficient implementation of a trust region method for box constrained optimization

Premium Partner