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Volumn 79, Issue 4, 2015, Pages 2251-2270

Complex dynamics of ecological systems under nonlinear harvesting: Hopf bifurcation and Turing instability

Author keywords

Harvesting; Holling type IV functional response; Hopf bifurcation; Pattern formation; Turing instability

Indexed keywords

HARVESTING; PREDATOR PREY SYSTEMS; STABILITY;

EID: 84925539531     PISSN: 0924090X     EISSN: 1573269X     Source Type: Journal    
DOI: 10.1007/s11071-014-1808-0     Document Type: Article
Times cited : (30)

References (32)
  • 1
    • 0036141801 scopus 로고    scopus 로고
    • Mutual interference between predators can give rise to Turing spatial patterns
    • Alonso, D., Bartumeus, F., Catalan, J.: Mutual interference between predators can give rise to Turing spatial patterns. Ecology 83(1), 28–34 (2002)
    • (2002) Ecology , vol.83 , Issue.1 , pp. 28-34
    • Alonso, D.1    Bartumeus, F.2    Catalan, J.3
  • 2
    • 84899904048 scopus 로고    scopus 로고
    • Spatiotemporal dynamics of a predator-prey system with linear harvesting rate
    • Baek, H.: Spatiotemporal dynamics of a predator-prey system with linear harvesting rate. Math. Probl. Eng. 2014, 1–9 (2014)
    • (2014) Math. Probl. Eng. , vol.2014 , pp. 1-9
    • Baek, H.1
  • 3
    • 79952535638 scopus 로고    scopus 로고
    • Tomography of reaction-diffusion microemulsions reveals three-dimensional Turing patterns
    • Bánsági, T., Vanag, V.K., Epstein, I.R.: Tomography of reaction-diffusion microemulsions reveals three-dimensional Turing patterns. Science 331(6022), 1309–1312 (2011)
    • (2011) Science , vol.331 , Issue.6022 , pp. 1309-1312
    • Bánsági, T.1    Vanag, V.K.2    Epstein, I.R.3
  • 4
    • 0033038309 scopus 로고    scopus 로고
    • A two-dimensional numerical study of spatial pattern formation in interacting Turing systems
    • Barrio, R.A., Varea, C., Aragn, J.L., Maini, P.K.: A two-dimensional numerical study of spatial pattern formation in interacting Turing systems. Bull. Math. Biol. 61(3), 483–505 (1999)
    • (1999) Bull. Math. Biol. , vol.61 , Issue.3 , pp. 483-505
    • Barrio, R.A.1    Varea, C.2    Aragn, J.L.3    Maini, P.K.4
  • 5
    • 70449709814 scopus 로고    scopus 로고
    • Turing and Hopf patterns formation in a predator-prey model with Leslie–Gower-type functional response
    • Camara, B.I., Aziz-Alaoui, M.A.: Turing and Hopf patterns formation in a predator-prey model with Leslie–Gower-type functional response. Dyn. Contin. Discret. Impuls. Syst. 16, 479–488 (2009)
    • (2009) Dyn. Contin. Discret. Impuls. Syst , vol.16 , pp. 479-488
    • Camara, B.I.1    Aziz-Alaoui, M.A.2
  • 9
    • 79955523591 scopus 로고    scopus 로고
    • Spatiotemporal dynamics of a Leslie–Gower predator-prey model incorporating a prey refuge. Nonlinear Anal
    • Guan, X., Wang, W., Cai, Y.: Spatiotemporal dynamics of a Leslie–Gower predator-prey model incorporating a prey refuge. Nonlinear Anal. Real World Appl. 12(4), 2385–2395 (2011)
    • (2011) Real World Appl , vol.12 , Issue.4 , pp. 2385-2395
    • Guan, X.1    Wang, W.2    Cai, Y.3
  • 10
    • 84867703142 scopus 로고    scopus 로고
    • Bifurcation analysis of modified Leslie–Gower predator-prey model with Michaelis-Menten type prey harvesting
    • Gupta, R.P., Chandra, P.: Bifurcation analysis of modified Leslie–Gower predator-prey model with Michaelis-Menten type prey harvesting. J. Math. Anal. Appl. 398(1), 278–295 (2013)
    • (2013) J. Math. Anal. Appl. , vol.398 , Issue.1 , pp. 278-295
    • Gupta, R.P.1    Chandra, P.2
  • 14
    • 84885970317 scopus 로고    scopus 로고
    • Bifurcation analysis in a predator-prey model with constant-yield predator harvesting
    • Huang, J., Gong, Y., & Ruan, S.: Bifurcation analysis in a predator-prey model with constant-yield predator harvesting. Discret. Contin. Dyn. Syst. Ser. B 18(8), 2101–2121 (2013)
    • (2013) Discret. Contin. Dyn. Syst. Ser. B , vol.18 , Issue.8 , pp. 2101-2121
    • Huang, J.1    Gong, Y.2    Ruan, S.3
  • 15
    • 84874233194 scopus 로고    scopus 로고
    • Kelley, J.L., Fitzpatrick, J.L., Merilaita, S.: Spots and stripes: ecology and colour pattern evolution in butterflyfishes. Proceedings of the Royal Society B: Biological Sciences 280(1757), 20122730 (2013)
    • Kelley, J.L., Fitzpatrick, J.L., Merilaita, S.: Spots and stripes: ecology and colour pattern evolution in butterflyfishes. Proceedings of the Royal Society B: Biological Sciences 280(1757), 20122730 (2013)
  • 16
    • 79955521200 scopus 로고    scopus 로고
    • Phase portraits, Hopf bifurcations and limit cycles of the Holling–Tanner models for predator-prey interactions
    • Lan, K.Q., Zhu, C.R.: Phase portraits, Hopf bifurcations and limit cycles of the Holling–Tanner models for predator-prey interactions. Nonlinear Anal. Real World Appl. 12(4), 1961–1973 (2011)
    • (2011) Nonlinear Anal. Real World Appl. , vol.12 , Issue.4 , pp. 1961-1973
    • Lan, K.Q.1    Zhu, C.R.2
  • 17
    • 84875676938 scopus 로고    scopus 로고
    • Hopf bifurcation and Turing instability in the reaction-diffusion HollingTanner predator-prey model. IMA
    • Li, X., Jiang, W., Shi, J.: Hopf bifurcation and Turing instability in the reaction-diffusion HollingTanner predator-prey model. IMA J. Appl. Math. 78(2), 287–306 (2013)
    • (2013) J. Appl. Math , vol.78 , Issue.2 , pp. 287-306
    • Li, X.1    Jiang, W.2    Shi, J.3
  • 18
    • 0000073691 scopus 로고
    • Qualitative analysis of insect outbreak systems: the spruce budworm and forest
    • Ludwig, D., Jones, D.D., Holling, C.S.: Qualitative analysis of insect outbreak systems: the spruce budworm and forest. J. Anim. Ecol. 47, 315–332 (1978)
    • (1978) J. Anim. Ecol. , vol.47 , pp. 315-332
    • Ludwig, D.1    Jones, D.D.2    Holling, C.S.3
  • 19
    • 33845326442 scopus 로고    scopus 로고
    • The Turing model comes of molecular age
    • Maini, P.K., Baker, R.E., Chuong, C.: The Turing model comes of molecular age. Sci. N. Y. Wash. 314, 1397–1398 (2006)
    • (2006) Sci. N. Y. Wash. , vol.314 , pp. 1397-1398
    • Maini, P.K.1    Baker, R.E.2    Chuong, C.3
  • 20
    • 0030697159 scopus 로고    scopus 로고
    • Spatial pattern formation in an insect host-parasitoid system
    • Maron, J.L., Harrison, S.: Spatial pattern formation in an insect host-parasitoid system. Science 278(5343), 1619–1621 (1997)
    • (1997) Science , vol.278 , Issue.5343 , pp. 1619-1621
    • Maron, J.L.1    Harrison, S.2
  • 21
    • 42949147760 scopus 로고    scopus 로고
    • Spatial pattern and ecological process in the coffee agroforestry system
    • Perfecto, I., Vandermeer, J.: Spatial pattern and ecological process in the coffee agroforestry system. Ecology 89(4), 915–920 (2008)
    • (2008) Ecology , vol.89 , Issue.4 , pp. 915-920
    • Perfecto, I.1    Vandermeer, J.2
  • 22
    • 84869995565 scopus 로고    scopus 로고
    • Complex population dynamics in heterogeneous environments: effects of random and directed animal movements
    • Rai, V., Upadhyay, R.K., Thakur, N.K.: Complex population dynamics in heterogeneous environments: effects of random and directed animal movements. Int. J. Nonlinear Sci. Numer. Simul. 13(3), 299–309 (2012)
    • (2012) Int. J. Nonlinear Sci. Numer. Simul. , vol.13 , Issue.3 , pp. 299-309
    • Rai, V.1    Upadhyay, R.K.2    Thakur, N.K.3
  • 23
    • 84899642462 scopus 로고    scopus 로고
    • Spatiotemporal complexity of a three-species ratio-dependent food chain model
    • Rao, F.: Spatiotemporal complexity of a three-species ratio-dependent food chain model. Nonlinear Dyn. 76(3), 1661–1676 (2014)
    • (2014) Nonlinear Dyn. , vol.76 , Issue.3 , pp. 1661-1676
    • Rao, F.1
  • 24
    • 84925496314 scopus 로고    scopus 로고
    • Dynamics of modified Leslie–Gower predator-prey model with predator harvesting
    • Saleh, K.: Dynamics of modified Leslie–Gower predator-prey model with predator harvesting. Int. J. Basic Appl. Sci. 13(4), 55–60 (2013)
    • (2013) Int. J. Basic Appl. Sci. , vol.13 , Issue.4 , pp. 55-60
    • Saleh, K.1
  • 25
    • 0001298002 scopus 로고
    • A simple plankton model
    • Steele, J.H., Henderson, E.W.: A simple plankton model. Am. Nat. 117, 676–691 (1981)
    • (1981) Am. Nat. , vol.117 , pp. 676-691
    • Steele, J.H.1    Henderson, E.W.2
  • 26
    • 84862871757 scopus 로고    scopus 로고
    • Pattern formation of a spatial predator-prey system
    • Sun, G.Q., Zhang, J., Song, L.P., Jin, Z., Li, B.L.: Pattern formation of a spatial predator-prey system. Appl. Math. Comput. 218(22), 11151–11162 (2012)
    • (2012) Appl. Math. Comput , vol.218 , Issue.22 , pp. 11151-11162
    • Sun, G.Q.1    Zhang, J.2    Song, L.P.3    Jin, Z.4    Li, B.L.5
  • 28
    • 84901066065 scopus 로고    scopus 로고
    • Dynamics of an epidemic model with spatial diffusion
    • Wang, T.: Dynamics of an epidemic model with spatial diffusion. Physica A Stat. Mech. Appl. 409, 119–129 (2014)
    • (2014) Physica A Stat. Mech. Appl. , vol.409 , pp. 119-129
    • Wang, T.1
  • 29
    • 34347224051 scopus 로고    scopus 로고
    • Spatiotemporal complexity of a ratio-dependent predator-prey system
    • Wang, W., Liu, Q.X., Jin, Z.: Spatiotemporal complexity of a ratio-dependent predator-prey system. Phys. Rev. E 75(5), 051913 (2007)
    • (2007) Phys. Rev. E , vol.75 , Issue.5 , pp. 051913
    • Wang, W.1    Liu, Q.X.2    Jin, Z.3
  • 31
    • 58749112528 scopus 로고    scopus 로고
    • Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
    • Yi, F., Wei, J., Shi, J.: Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system. J. Differ. Equ. 246(5), 1944–1977 (2009)
    • (2009) J. Differ. Equ , vol.246 , Issue.5 , pp. 1944-1977
    • Yi, F.1    Wei, J.2    Shi, J.3
  • 32
    • 84925510211 scopus 로고    scopus 로고
    • Spatio-temporal dynamics of a reaction-diffusion system for a predator-prey model with hyperbolic mortality
    • Zhang, T., Xing, Y., Zang, H., Han, M.: Spatio-temporal dynamics of a reaction-diffusion system for a predator-prey model with hyperbolic mortality. Nonlinear Dyn. 77, 1–13 (2014)
    • (2014) Nonlinear Dyn , vol.77 , pp. 1-13
    • Zhang, T.1    Xing, Y.2    Zang, H.3    Han, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.