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Volumn 18, Issue 8, 2008, Pages 2223-2248

Bifurcations, and temporal and spatial patterns of a modified Lotka-Volterra model

Author keywords

Bistability; Bogdanov Takens bifurcation; Bursting oscillations; Localized structures; Predator prey model; Prey dependent functional response; Turing patterns

Indexed keywords

BIFURCATION (MATHEMATICS); DYNAMICS; ECOLOGY; HOPF BIFURCATION; NUMERICAL METHODS; OPTICAL BISTABILITY;

EID: 54949098474     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127408021671     Document Type: Article
Times cited : (37)

References (41)
  • 1
    • 13244288118 scopus 로고    scopus 로고
    • Plant-herbivore models, where more grass means fewer grazers
    • Barnes. B. & Sidhu, H. [2005] "Plant-herbivore models, where more grass means fewer grazers," Bull. Math, Biol. 67, 33-55.
    • (2005) Bull. Math, Biol , vol.67 , pp. 33-55
    • Barnes, B.1    Sidhu, H.2
  • 2
    • 3042890893 scopus 로고
    • Sistema Volterra i uravnenie Mihaelis-Menten
    • Nauka Novosibirsk, Russia, pp
    • Bazykin, A. D. [1974] "Sistema Volterra i uravnenie Mihaelis-Menten," in Voprosy Matematicheskoy Genetiki (Nauka Novosibirsk, Russia), pp. 103-143.
    • (1974) Voprosy Matematicheskoy Genetiki , pp. 103-143
    • Bazykin, A.D.1
  • 4
    • 0029303855 scopus 로고
    • Topological and phenomenological classification of bursting oscillations
    • Bertram, R., Butte, M. J., Kiemel, T. & Sherman, A. [1995] "Topological and phenomenological classification of bursting oscillations," Bull. Math. Biol. 57, 413-439.
    • (1995) Bull. Math. Biol , vol.57 , pp. 413-439
    • Bertram, R.1    Butte, M.J.2    Kiemel, T.3    Sherman, A.4
  • 5
    • 0000971882 scopus 로고
    • Turing bifurcations and pattern selection
    • eds. Kapral, K. & Showalter, K, Kluwer, Dordrecht
    • Borckmans, P., Dewel, G., DeWit, A. & Walgraef. D., [1995] "Turing bifurcations and pattern selection," in Chemical Waves and Patterns, eds. Kapral, K. & Showalter, K. (Kluwer, Dordrecht).
    • (1995) Chemical Waves and Patterns
    • Borckmans, P.1    Dewel, G.2    DeWit, A.3    Walgraef, D.4
  • 6
    • 0020807390 scopus 로고
    • Amplitude equations for systems with competing instabilities
    • Coullet, P. H. & Spiegel, E. A. [1983] "Amplitude equations for systems with competing instabilities," SIAM J. Appl. Math. 43, 776-821.
    • (1983) SIAM J. Appl. Math , vol.43 , pp. 776-821
    • Coullet, P.H.1    Spiegel, E.A.2
  • 8
    • 54949098607 scopus 로고    scopus 로고
    • eds. Hasselblatt, B. & Katok, A, Elsevier, NY, p
    • Guckenheimer, J. [2002] Handbook of Dynamical Systems, eds. Hasselblatt, B. & Katok, A. (Elsevier, NY), p. 378.
    • (2002) Handbook of Dynamical Systems , pp. 378
    • Guckenheimer, J.1
  • 9
    • 24544442979 scopus 로고
    • Pattern formation in the presence of symmetries
    • Gunaratne, G. H., Ouyang, Q. & Swinney, H. L. [1994] "Pattern formation in the presence of symmetries," Phys. Rev. E 50, 2802.
    • (1994) Phys. Rev. E , vol.50 , pp. 2802
    • Gunaratne, G.H.1    Ouyang, Q.2    Swinney, H.L.3
  • 10
    • 0025956240 scopus 로고
    • Chaos in a threespecies food chain
    • Hastings, A. & Powell, T. [1991] "Chaos in a threespecies food chain," Ecology 72, 896-903.
    • (1991) Ecology , vol.72 , pp. 896-903
    • Hastings, A.1    Powell, T.2
  • 11
    • 0002366911 scopus 로고
    • The functional response of predator to prey density and its role in mimicry and population regulation
    • Holling, C. S. [1965] "The functional response of predator to prey density and its role in mimicry and population regulation," Mem. Entomol. Soc. Can. 45, 1-60.
    • (1965) Mem. Entomol. Soc. Can , vol.45 , pp. 1-60
    • Holling, C.S.1
  • 12
    • 0000303940 scopus 로고    scopus 로고
    • Neural stability, spiking and burstanding
    • Izhikevich, E. M. [2000] "Neural stability, spiking and burstanding," Intr. J. Bifurcation and Chaos 6, 1171-1266.
    • (2000) Intr. J. Bifurcation and Chaos , vol.6 , pp. 1171-1266
    • Izhikevich, E.M.1
  • 14
    • 0000401570 scopus 로고
    • Localized structures and front propagation in the Lengyel-Epstein model
    • Jensen, O., Pannbacker, V. O., Moselkilde, E., Dewel, G. & Borkcmans, P. [1994] "Localized structures and front propagation in the Lengyel-Epstein model," Phy. Rev. E 50 736-749.
    • (1994) Phy. Rev. E , vol.50 , pp. 736-749
    • Jensen, O.1    Pannbacker, V.O.2    Moselkilde, E.3    Dewel, G.4    Borkcmans, P.5
  • 19
    • 33746076074 scopus 로고
    • Contribution to the theory of periodic reactions
    • Lotka, A. J. [1910] "Contribution to the theory of periodic reactions," J. Phys. Chem. 14, 271-274.
    • (1910) J. Phys. Chem , vol.14 , pp. 271-274
    • Lotka, A.J.1
  • 20
    • 0001620238 scopus 로고
    • Analytical note on certain rhythmic relations in organic systems
    • Lotka, A. J. [1920a] "Analytical note on certain rhythmic relations in organic systems," Proc. Nat. Acad. Sci. U.S. 6, 410-415.
    • (1920) Proc. Nat. Acad. Sci. U.S , vol.6 , pp. 410-415
    • Lotka, A.J.1
  • 21
    • 33846837061 scopus 로고
    • Undamped oscillations derived from the law of mass action
    • Lotka. A. J. [1920b] "Undamped oscillations derived from the law of mass action," J. Am. Chem. Soc. 42, 1595-1599.
    • (1920) J. Am. Chem. Soc , vol.42 , pp. 1595-1599
    • Lotka, A.J.1
  • 22
    • 20444460353 scopus 로고    scopus 로고
    • McGehee, E. A. & Peacock-López, E. [2005] Turing patterns in a modified Lotka-Volterra Model, Phys. Lett. A 342, 90-98.
    • McGehee, E. A. & Peacock-López, E. [2005] "Turing patterns in a modified Lotka-Volterra Model," Phys. Lett. A 342, 90-98.
  • 24
    • 0036161027 scopus 로고    scopus 로고
    • Transient dynamics and pattern formation: Reactivity is necessary for Turing instabilities
    • Neubert, M. G., Caswell, H. & Murray, J. D. [2002] "Transient dynamics and pattern formation: Reactivity is necessary for Turing instabilities," Math. Biosci. 175, 1-11.
    • (2002) Math. Biosci , vol.175 , pp. 1-11
    • Neubert, M.G.1    Caswell, H.2    Murray, J.D.3
  • 25
    • 3543132482 scopus 로고    scopus 로고
    • Reactivity and transient dynamics of prey-predator and food web models
    • Neubert, M. G., Klanjscek, T. & Caswell, H. [2004] "Reactivity and transient dynamics of prey-predator and food web models," Ecol. Model. 179, 29-38.
    • (2004) Ecol. Model , vol.179 , pp. 29-38
    • Neubert, M.G.1    Klanjscek, T.2    Caswell, H.3
  • 26
    • 11944269782 scopus 로고
    • Localized traveling-wave states in binary-fluid convection
    • Niemcla, J.J., Ahlers, G. & Cannell, D. S. [1990] "Localized traveling-wave states in binary-fluid convection," Phys. Rev. Lett. 64, 1365-1368.
    • (1990) Phys. Rev. Lett , vol.64 , pp. 1365-1368
    • Niemcla, J.J.1    Ahlers, G.2    Cannell, D.S.3
  • 28
    • 9644310636 scopus 로고    scopus 로고
    • Ecological model of competitive species and the role of intraspecies interaction in the formation of spatio-temporal patterns
    • Peacock-López, E. [2004] "Ecological model of competitive species and the role of intraspecies interaction in the formation of spatio-temporal patterns," WSEAS Trans. Bio. Biomed. 1, 76-81.
    • (2004) WSEAS Trans. Bio. Biomed , vol.1 , pp. 76-81
    • Peacock-López, E.1
  • 29
    • 9644302359 scopus 로고    scopus 로고
    • Complex dynamics in a three-level trophic system with intraspecies interactions
    • Peet, A. B., Deutsch, P. A. & Peacock-López, E. [2005] "Complex dynamics in a three-level trophic system with intraspecies interactions," J. Theo. Biol. 232, 491-503.
    • (2005) J. Theo. Biol , vol.232 , pp. 491-503
    • Peet, A.B.1    Deutsch, P.A.2    Peacock-López, E.3
  • 30
    • 54949133806 scopus 로고    scopus 로고
    • Press, W. H., Flannery, B. P., Teukolsky, S. A & Vetterling, W. T. [1992] Numerical Recipes in FOR- TRAN: The Art of Scientific Computing, 2nd edn. (Cambridge University Press, Cambridge, England).
    • Press, W. H., Flannery, B. P., Teukolsky, S. A & Vetterling, W. T. [1992] Numerical Recipes in FOR- TRAN: The Art of Scientific Computing, 2nd edn. (Cambridge University Press, Cambridge, England).
  • 31
    • 0001524523 scopus 로고
    • Graphical representation and stability condition of predator-prey interaction
    • Rosenzweig, M. L. & MacArthur. R. H. [1963] "Graphical representation and stability condition of predator-prey interaction," Amer. Naturalist 97, 209-223.
    • (1963) Amer. Naturalist , vol.97 , pp. 209-223
    • Rosenzweig, M.L.1    MacArthur, R.H.2
  • 32
    • 5244375340 scopus 로고
    • Selforganization induced by the differential flow of activator and inhibitor
    • Rovinsky, A. B. & Menzinger, M. [1993] "Selforganization induced by the differential flow of activator and inhibitor," Phys. Rev. Lett. 70, 778-781.
    • (1993) Phys. Rev. Lett , vol.70 , pp. 778-781
    • Rovinsky, A.B.1    Menzinger, M.2
  • 33
    • 0018519322 scopus 로고
    • Efficient Fortran subprograms for the solution of separable elliptic partial differential equations
    • Swartrauber, P. N. & Seet, R. A. [1979] "Efficient Fortran subprograms for the solution of separable elliptic partial differential equations," ACM Trans. Math. Soft. 5, 352-364.
    • (1979) ACM Trans. Math. Soft , vol.5 , pp. 352-364
    • Swartrauber, P.N.1    Seet, R.A.2
  • 34
    • 0033717678 scopus 로고    scopus 로고
    • Patterns and localized structures in bistable semiconductor resonators
    • Taranenko, V. I., Ganne, I., Kuszelewicz, R. J. & Weiss, C. O. [2000] "Patterns and localized structures in bistable semiconductor resonators," Phys. Rev. A 61, 063818.
    • (2000) Phys. Rev. A , vol.61 , pp. 063818
    • Taranenko, V.I.1    Ganne, I.2    Kuszelewicz, R.J.3    Weiss, C.O.4
  • 35
    • 0028494346 scopus 로고
    • Localized structures and localized patterns in optical bistability
    • Tlidi, M., Mandel, P., & Lefever, R. [1994] "Localized structures and localized patterns in optical bistability," Phys. Rev. Lett. 73, 640-643.
    • (1994) Phys. Rev. Lett , vol.73 , pp. 640-643
    • Tlidi, M.1    Mandel, P.2    Lefever, R.3
  • 37
    • 2342596966 scopus 로고    scopus 로고
    • Stationary and oscillatory localized patterns, and subcritical bifurcations
    • Vanag, V. K. & Epstein, I. R. [2004] "Stationary and oscillatory localized patterns, and subcritical bifurcations," Phys. Rev. Lett. 92, 128301.
    • (2004) Phys. Rev. Lett , vol.92 , pp. 128301
    • Vanag, V.K.1    Epstein, I.R.2
  • 38
    • 0006170098 scopus 로고
    • Fluctuations in the abundance of a species considered mathematically
    • Volterra, V. [1926a] "Fluctuations in the abundance of a species considered mathematically," Nature 118, 558-560.
    • (1926) Nature , vol.118 , pp. 558-560
    • Volterra, V.1
  • 39
    • 0002604954 scopus 로고
    • Variazioni e fluttuazioni del numero d'individui in specie animali conviventi
    • Volterra, V. [1926b] "Variazioni e fluttuazioni del numero d'individui in specie animali conviventi," Mem. Acad, Lincei. 2, 31-113.
    • (1926) Mem. Acad, Lincei , vol.2 , pp. 31-113
    • Volterra, V.1
  • 41
    • 18344411338 scopus 로고    scopus 로고
    • Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes
    • Yang, L. F. Dolnik, M., Zhabotinsky, A. M. & Epstein, I. R. [2002] "Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes," Phys. Rev. Lett. 88, 208303.
    • (2002) Phys. Rev. Lett , vol.88 , pp. 208303
    • Yang, L.F.1    Dolnik, M.2    Zhabotinsky, A.M.3    Epstein, I.R.4


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