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Volumn 39, Issue 4, 2009, Pages 1883-1895

Bifurcation and chaos in a ratio-dependent predator-prey system with time delay

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; HOPF BIFURCATION; TIME DELAY; TIMING CIRCUITS;

EID: 63449103219     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.06.122     Document Type: Article
Times cited : (37)

References (40)
  • 1
    • 4944258042 scopus 로고
    • Coupling in predator-prey dynamics: ratio-dependence
    • Arditi R., and Ginzburg L.R. Coupling in predator-prey dynamics: ratio-dependence. J Theor Biol 139 (1989) 311-326
    • (1989) J Theor Biol , vol.139 , pp. 311-326
    • Arditi, R.1    Ginzburg, L.R.2
  • 2
    • 0000542895 scopus 로고
    • Variation in plankton densities among lakes: a case for ratio-dependent models
    • Arditi R., Ginzburg L.R., and Akcakaya H.R. Variation in plankton densities among lakes: a case for ratio-dependent models. Am Nat 138 (1991) 287-1296
    • (1991) Am Nat , vol.138 , pp. 287-1296
    • Arditi, R.1    Ginzburg, L.R.2    Akcakaya, H.R.3
  • 3
    • 0025946035 scopus 로고
    • Functional response and heterogeneities: an experiment test with cladocerans
    • Arditi R., Perrin N., and Saiah H. Functional response and heterogeneities: an experiment test with cladocerans. OIKOS 60 (1991) 9-75
    • (1991) OIKOS , vol.60 , pp. 9-75
    • Arditi, R.1    Perrin, N.2    Saiah, H.3
  • 4
    • 0027100815 scopus 로고
    • Empirical evidence of the role of heterogeneity in ratio-dependent consumption
    • Arditi R., and Saiah H. Empirical evidence of the role of heterogeneity in ratio-dependent consumption. Ecology 73 (1992) 544-1551
    • (1992) Ecology , vol.73 , pp. 544-1551
    • Arditi, R.1    Saiah, H.2
  • 5
  • 6
    • 0031468520 scopus 로고    scopus 로고
    • Permanence of population growth models with impulsive effects
    • Ballinger G., and Liu X. Permanence of population growth models with impulsive effects. Math Comput Modell 26 (1997) 9-72
    • (1997) Math Comput Modell , vol.26 , pp. 9-72
    • Ballinger, G.1    Liu, X.2
  • 7
    • 0032058512 scopus 로고    scopus 로고
    • Global analyses in some delayed ratio-dependent predator-prey systems
    • Beretta E., and Kuang Y. Global analyses in some delayed ratio-dependent predator-prey systems. Nonlinear Anal 32 (1998) 81-408
    • (1998) Nonlinear Anal , vol.32 , pp. 81-408
    • Beretta, E.1    Kuang, Y.2
  • 8
    • 0035460669 scopus 로고    scopus 로고
    • Parametric analysis of the ratio-dependent predator-prey model
    • Berezovskaya F., Karev G., and Arditi R. Parametric analysis of the ratio-dependent predator-prey model. J Math Biol 43 (2001) 21-246
    • (2001) J Math Biol , vol.43 , pp. 21-246
    • Berezovskaya, F.1    Karev, G.2    Arditi, R.3
  • 9
    • 33747346741 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation analysis in a three-level food chain system with delay
    • Chen Y., Yu J., and Sun C. Stability and Hopf bifurcation analysis in a three-level food chain system with delay. Chaos, Solitons & Fractals 31 (2007) 83-694
    • (2007) Chaos, Solitons & Fractals , vol.31 , pp. 83-694
    • Chen, Y.1    Yu, J.2    Sun, C.3
  • 10
    • 0036291194 scopus 로고    scopus 로고
    • Stability properties of pulse vaccination strategy in SEIR epidemic model
    • D'Onofrio A. Stability properties of pulse vaccination strategy in SEIR epidemic model. Math Biosci 179 (2002) 7-72
    • (2002) Math Biosci , vol.179 , pp. 7-72
    • D'Onofrio, A.1
  • 11
    • 0042793280 scopus 로고    scopus 로고
    • Periodicity in a delayed ratio-dependent predator-prey system
    • Fan M., and Wang K. Periodicity in a delayed ratio-dependent predator-prey system. J Math Anal Appl 262 (2001) 179-190
    • (2001) J Math Anal Appl , vol.262 , pp. 179-190
    • Fan, M.1    Wang, K.2
  • 12
    • 0027084787 scopus 로고
    • The physiological basis of ratio-dependent predator-prey theory: a metabolic pool model of Nicholson's blowflies as an example
    • Gutierrez A.P. The physiological basis of ratio-dependent predator-prey theory: a metabolic pool model of Nicholson's blowflies as an example. Ecology 73 (1992) 1552-1563
    • (1992) Ecology , vol.73 , pp. 1552-1563
    • Gutierrez, A.P.1
  • 14
    • 0001397558 scopus 로고
    • The functional response of predator: worries about scale
    • Hanski I. The functional response of predator: worries about scale. TREE 6 (1991) 41-142
    • (1991) TREE , vol.6 , pp. 41-142
    • Hanski, I.1
  • 16
    • 0035376255 scopus 로고    scopus 로고
    • Global analysis of the Michaelis-Menten ratio-dependent predator-prey system
    • Hsu S.B., Hwang T.W., and Kuang Y. Global analysis of the Michaelis-Menten ratio-dependent predator-prey system. J Math Biol 42 (2001) 489-506
    • (2001) J Math Biol , vol.42 , pp. 489-506
    • Hsu, S.B.1    Hwang, T.W.2    Kuang, Y.3
  • 17
    • 0035512366 scopus 로고    scopus 로고
    • Rich dynamics of a ratio-dependent one prey two predator model
    • Hsu S.B., Hwang T.W., and Kuang Y. Rich dynamics of a ratio-dependent one prey two predator model. J Math Biol 43 (2001) 377-396
    • (2001) J Math Biol , vol.43 , pp. 377-396
    • Hsu, S.B.1    Hwang, T.W.2    Kuang, Y.3
  • 18
    • 4644296135 scopus 로고    scopus 로고
    • Bifurcation analysis in a limit cycle oscillator with delayed feedback
    • Jiang W., and Wei J. Bifurcation analysis in a limit cycle oscillator with delayed feedback. Chaos, Solitons & Fractals 23 (2005) 817-831
    • (2005) Chaos, Solitons & Fractals , vol.23 , pp. 817-831
    • Jiang, W.1    Wei, J.2
  • 20
    • 0000252357 scopus 로고    scopus 로고
    • Global qualitative analysis of a ratio-dependent predator-prey system
    • Kuang Y., and Beretta E. Global qualitative analysis of a ratio-dependent predator-prey system. J Math Biol 36 (1998) 389-406
    • (1998) J Math Biol , vol.36 , pp. 389-406
    • Kuang, Y.1    Beretta, E.2
  • 21
    • 0347269498 scopus 로고    scopus 로고
    • Bifurcation of nontrivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment
    • Lakmeche A., and Arino O. Bifurcation of nontrivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment. Dyn Continuous, Discrete Impulsive Syst 7 (2000) 265-287
    • (2000) Dyn Continuous, Discrete Impulsive Syst , vol.7 , pp. 265-287
    • Lakmeche, A.1    Arino, O.2
  • 23
    • 2042474111 scopus 로고    scopus 로고
    • Hopf bifurcations in a Volterra prey-predator model with strong kernel
    • Li S., Liao X., and Li C. Hopf bifurcations in a Volterra prey-predator model with strong kernel. Chaos, Solitons & Fractals 22 (2004) 713-722
    • (2004) Chaos, Solitons & Fractals , vol.22 , pp. 713-722
    • Li, S.1    Liao, X.2    Li, C.3
  • 24
    • 24944487530 scopus 로고    scopus 로고
    • Stability and Hopf bifurcations in a harvested one-prey-two-predator model with delays
    • Liu Z., and Yuan R. Stability and Hopf bifurcations in a harvested one-prey-two-predator model with delays. Chaos, Solitons & Fractals 27 (2006) 1395-1407
    • (2006) Chaos, Solitons & Fractals , vol.27 , pp. 1395-1407
    • Liu, Z.1    Yuan, R.2
  • 25
    • 1342264354 scopus 로고    scopus 로고
    • Stability and Hopf bifurcations of mutual system with time delay
    • Meng X., and Wei J. Stability and Hopf bifurcations of mutual system with time delay. Chaos, Solitons & Fractals 21 (2004) 729-740
    • (2004) Chaos, Solitons & Fractals , vol.21 , pp. 729-740
    • Meng, X.1    Wei, J.2
  • 26
    • 0030140255 scopus 로고    scopus 로고
    • A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competitive environment
    • Panetta J.C. A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competitive environment. Bull Math Biol 58 (1996) 425-447
    • (1996) Bull Math Biol , vol.58 , pp. 425-447
    • Panetta, J.C.1
  • 27
    • 0031750774 scopus 로고    scopus 로고
    • The dynamics of an infectious disease in a population with birth pulses
    • Roberts M.G., and Kao R.R. The dynamics of an infectious disease in a population with birth pulses. Math Biosci 149 (1998) 23-36
    • (1998) Math Biosci , vol.149 , pp. 23-36
    • Roberts, M.G.1    Kao, R.R.2
  • 28
    • 0032213158 scopus 로고    scopus 로고
    • Pulse vaccination strategy in the SIR epidemic model
    • Shulgin B., Stone L., and Agur Z. Pulse vaccination strategy in the SIR epidemic model. Bull Math Biol 60 (1998) 1123-1148
    • (1998) Bull Math Biol , vol.60 , pp. 1123-1148
    • Shulgin, B.1    Stone, L.2    Agur, Z.3
  • 29
    • 2942638131 scopus 로고    scopus 로고
    • Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays
    • Song Y., Han M., and Peng Y. Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays. Chaos, Solitons & Fractals 22 (2004) 1139-1148
    • (2004) Chaos, Solitons & Fractals , vol.22 , pp. 1139-1148
    • Song, Y.1    Han, M.2    Peng, Y.3
  • 30
    • 12244261643 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays
    • Song Y., Han M., and Wei J. Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays. Physica D 200 (2005) 185-204
    • (2005) Physica D , vol.200 , pp. 185-204
    • Song, Y.1    Han, M.2    Wei, J.3
  • 31
    • 1842581482 scopus 로고    scopus 로고
    • Bifurcation analysis for Chen's system with delayed feedback and its application to control of chaos
    • Song Y., and Wei J. Bifurcation analysis for Chen's system with delayed feedback and its application to control of chaos. Chaos, Solitons & Fractals 22 (2004) 75-91
    • (2004) Chaos, Solitons & Fractals , vol.22 , pp. 75-91
    • Song, Y.1    Wei, J.2
  • 32
    • 33646146409 scopus 로고    scopus 로고
    • Stability and Hopf bifurcations for an epidemic disease model with delay
    • Sun C., Lin Y., and Han M. Stability and Hopf bifurcations for an epidemic disease model with delay. Chaos, Solitons & Fractals 30 (2006) 204-216
    • (2006) Chaos, Solitons & Fractals , vol.30 , pp. 204-216
    • Sun, C.1    Lin, Y.2    Han, M.3
  • 33
    • 33646146409 scopus 로고    scopus 로고
    • Analysis of stability and Hopf bifurcations for an epidemic disease model with delay
    • Sun C., Lin Y., and Han M. Analysis of stability and Hopf bifurcations for an epidemic disease model with delay. Chaos, Solitons & Fractals 30 (2006) 204-216
    • (2006) Chaos, Solitons & Fractals , vol.30 , pp. 204-216
    • Sun, C.1    Lin, Y.2    Han, M.3
  • 34
    • 33747368237 scopus 로고    scopus 로고
    • Analysis of stability and Hopf bifurcations for a delayed logistic equation
    • Sun C., Han M., and Lin Y. Analysis of stability and Hopf bifurcations for a delayed logistic equation. Chaos, Solitons & Fractals 31 (2007) 672-682
    • (2007) Chaos, Solitons & Fractals , vol.31 , pp. 672-682
    • Sun, C.1    Han, M.2    Lin, Y.3
  • 35
    • 0036483349 scopus 로고    scopus 로고
    • Density-dependent birth rate, birth pulses and their population dynamic consequences
    • Tang S., and Chen L. Density-dependent birth rate, birth pulses and their population dynamic consequences. J Math Biol 44 (2002) 185-199
    • (2002) J Math Biol , vol.44 , pp. 185-199
    • Tang, S.1    Chen, L.2
  • 36
    • 22844435930 scopus 로고    scopus 로고
    • Bifurcation and complexity of Monod type predator-prey system in a pulsed chemostat
    • Wang F., Zhang S., Chen L., and Sun L. Bifurcation and complexity of Monod type predator-prey system in a pulsed chemostat. Chaos, Solitons & Fractals 27 (2006) 447-458
    • (2006) Chaos, Solitons & Fractals , vol.27 , pp. 447-458
    • Wang, F.1    Zhang, S.2    Chen, L.3    Sun, L.4
  • 37
    • 2342442918 scopus 로고    scopus 로고
    • Hopf bifurcation in bidirectional associative memory neural network with delays: analysis and computation
    • Wang L., and Zou X. Hopf bifurcation in bidirectional associative memory neural network with delays: analysis and computation. J Comput Appl Math 167 (2004) 73-90
    • (2004) J Comput Appl Math , vol.167 , pp. 73-90
    • Wang, L.1    Zou, X.2
  • 38
    • 0034249333 scopus 로고    scopus 로고
    • Persistence and stability for a two-species ratio-dependent predator-prey system with time delay in a two-patch environment
    • Xu R., and Chen L. Persistence and stability for a two-species ratio-dependent predator-prey system with time delay in a two-patch environment. Comput Math Appl 40 (2000) 577-588
    • (2000) Comput Math Appl , vol.40 , pp. 577-588
    • Xu, R.1    Chen, L.2
  • 39
    • 0036868468 scopus 로고    scopus 로고
    • Persistence and global stability for n-species ratio-dependent predator-prey system with time delays
    • Xu R., and Chen L. Persistence and global stability for n-species ratio-dependent predator-prey system with time delays. J Math Anal Appl 275 (2002) 27-43
    • (2002) J Math Anal Appl , vol.275 , pp. 27-43
    • Xu, R.1    Chen, L.2
  • 40
    • 0036833143 scopus 로고    scopus 로고
    • Stability and Hopf bifurcations for a delay competition diffusion system
    • Zhou L., Tang Y., and Hussein S. Stability and Hopf bifurcations for a delay competition diffusion system. Chaos, Solitons & Fractals 14 (2002) 1201-1225
    • (2002) Chaos, Solitons & Fractals , vol.14 , pp. 1201-1225
    • Zhou, L.1    Tang, Y.2    Hussein, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.