메뉴 건너뛰기




Volumn 72, Issue 2, 2007, Pages 197-213

Bifurcation analysis of piecewise smooth ecological models

Author keywords

Bifurcation analysis; Filippov systems; Prey predator systems; Renewable resources management; Sliding

Indexed keywords

ANALYTICAL METHOD; ECOLOGICAL MODELING; POPULATION STRUCTURE; PREDATOR-PREY INTERACTION; SLIDING;

EID: 34547688858     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2007.06.003     Document Type: Article
Times cited : (80)

References (67)
  • 1
    • 0034503328 scopus 로고    scopus 로고
    • The evolution of predator-prey interactions: theory and evidence
    • Abrams P.A. The evolution of predator-prey interactions: theory and evidence. Annu. Rev. Ecol. Syst. 31 (2000) 79-105
    • (2000) Annu. Rev. Ecol. Syst. , vol.31 , pp. 79-105
    • Abrams, P.A.1
  • 3
    • 0001842302 scopus 로고    scopus 로고
    • Homoclinic and heteroclinic orbits in a tri-trophic food chain
    • Boer M., Kooi B., and Kooijman S. Homoclinic and heteroclinic orbits in a tri-trophic food chain. J. Math. Biol. 39 (1999) 19-38
    • (1999) J. Math. Biol. , vol.39 , pp. 19-38
    • Boer, M.1    Kooi, B.2    Kooijman, S.3
  • 4
    • 0007325771 scopus 로고    scopus 로고
    • Lyapunov functions for Lotka-Volterra predator-prey models with optimal foraging behaviour
    • Boukal D.S., and Křivan V. Lyapunov functions for Lotka-Volterra predator-prey models with optimal foraging behaviour. J. Math. Biol. 39 (1999) 493-517
    • (1999) J. Math. Biol. , vol.39 , pp. 493-517
    • Boukal, D.S.1    Křivan, V.2
  • 6
    • 0041757877 scopus 로고    scopus 로고
    • Structural stability of piecewise smooth systems
    • Broucke M., Pugh C.C., and Simic S.N. Structural stability of piecewise smooth systems. Comput. Appl. Math. 20 1-2 (2001) 51-90
    • (2001) Comput. Appl. Math. , vol.20 , Issue.1-2 , pp. 51-90
    • Broucke, M.1    Pugh, C.C.2    Simic, S.N.3
  • 7
    • 0000832921 scopus 로고
    • Optimal foraging: attack strategy of a mantid
    • Charnov E.L. Optimal foraging: attack strategy of a mantid. Am. Nat. 101 (1976) 141-151
    • (1976) Am. Nat. , vol.101 , pp. 141-151
    • Charnov, E.L.1
  • 8
    • 0342680045 scopus 로고    scopus 로고
    • Destabilising effect of period harvest on population dynamics
    • Chau N.P. Destabilising effect of period harvest on population dynamics. Ecol. Model. 127 (2000) 1-9
    • (2000) Ecol. Model. , vol.127 , pp. 1-9
    • Chau, N.P.1
  • 9
    • 0001747368 scopus 로고
    • Uniqueness of a limit cycle for a predator-prey system
    • Cheng K.S. Uniqueness of a limit cycle for a predator-prey system. SIAM J. Math. Anal. 12 (1981) 541-548
    • (1981) SIAM J. Math. Anal. , vol.12 , pp. 541-548
    • Cheng, K.S.1
  • 10
    • 33646247005 scopus 로고    scopus 로고
    • Application of a threshold policy in the management of multispecies fisheries and predator culling
    • Costa M.I.S., and Meza M.E.M. Application of a threshold policy in the management of multispecies fisheries and predator culling. Math. Med. Biol. 23 (2006) 63-75
    • (2006) Math. Med. Biol. , vol.23 , pp. 63-75
    • Costa, M.I.S.1    Meza, M.E.M.2
  • 12
    • 0032004760 scopus 로고    scopus 로고
    • Singular homoclinic bifurcations in tri-trophic food chains
    • De Feo O., and Rinaldi S. Singular homoclinic bifurcations in tri-trophic food chains. Math. Biosci. 148 (1998) 7-20
    • (1998) Math. Biosci. , vol.148 , pp. 7-20
    • De Feo, O.1    Rinaldi, S.2
  • 13
    • 17644394865 scopus 로고    scopus 로고
    • Department of Mathematics, Utrecht University, The Netherlands
    • Dercole F., and Kuznetsov Yu.A. User Guide to Slidecont 2.0 (2004), Department of Mathematics, Utrecht University, The Netherlands. 〈http://www.math.uu.nl/people/kuznet/cm/slidecont.pdf〉
    • (2004) User Guide to Slidecont 2.0
    • Dercole, F.1    Kuznetsov, Yu.A.2
  • 14
    • 17644403511 scopus 로고    scopus 로고
    • SlideCont: An Auto97 Driver for Bifurcation Analysis of Filippov Systems
    • Dercole F., and Kuznetsov Yu.A. SlideCont: An Auto97 Driver for Bifurcation Analysis of Filippov Systems. ACM Trans. Math. Soft. 31 (2005) 95-119
    • (2005) ACM Trans. Math. Soft. , vol.31 , pp. 95-119
    • Dercole, F.1    Kuznetsov, Yu.A.2
  • 16
    • 34248647895 scopus 로고    scopus 로고
    • Coevolution of slow-fast populations: an application to prey-predator systems
    • Dercole F., Gragnani A., Ferrière R., and Rinaldi S. Coevolution of slow-fast populations: an application to prey-predator systems. Proc. R. Soc. London B. 273 (2006) 983-990
    • (2006) Proc. R. Soc. London B. , vol.273 , pp. 983-990
    • Dercole, F.1    Gragnani, A.2    Ferrière, R.3    Rinaldi, S.4
  • 17
    • 0041822709 scopus 로고    scopus 로고
    • Grazing, skipping and sliding: analysis of the nonsmooth dynamics of the DC/DC buck converter
    • di Bernardo M., Champneys A., and Budd C. Grazing, skipping and sliding: analysis of the nonsmooth dynamics of the DC/DC buck converter. Nonlinearity 11 (1998) 858-890
    • (1998) Nonlinearity , vol.11 , pp. 858-890
    • di Bernardo, M.1    Champneys, A.2    Budd, C.3
  • 19
    • 0033229544 scopus 로고    scopus 로고
    • Local analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems
    • di Bernardo M., Feigin M.I., Hogan S., and Homer M. Local analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems. Chaos Solitons Fractals 10 (1999) 1881-1908
    • (1999) Chaos Solitons Fractals , vol.10 , pp. 1881-1908
    • di Bernardo, M.1    Feigin, M.I.2    Hogan, S.3    Homer, M.4
  • 20
    • 0035911618 scopus 로고    scopus 로고
    • Unified framework for the analysis of grazing and border-collision in piecewise-smooth systems
    • di Bernardo M., Budd C., and Champneys A. Unified framework for the analysis of grazing and border-collision in piecewise-smooth systems. Phys. Rev. Lett. 86 (2001) 2554-2556
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 2554-2556
    • di Bernardo, M.1    Budd, C.2    Champneys, A.3
  • 21
    • 0037105976 scopus 로고    scopus 로고
    • Bifurcations of dynamical systems with sliding: derivation of normal-form mappings
    • di Bernardo M., Kowalczyk P., and Nordmark A. Bifurcations of dynamical systems with sliding: derivation of normal-form mappings. Physica D 11 (2002) 175-205
    • (2002) Physica D , vol.11 , pp. 175-205
    • di Bernardo, M.1    Kowalczyk, P.2    Nordmark, A.3
  • 22
    • 0346910377 scopus 로고    scopus 로고
    • Sliding bifurcations: a novel mechanism for the sudden onset of chaos in dry-friction oscillators
    • di Bernardo M., Kowalczyk P., and Nordmark A. Sliding bifurcations: a novel mechanism for the sudden onset of chaos in dry-friction oscillators. Int. J. Bifurcation Chaos 13 (2003) 2935-2948
    • (2003) Int. J. Bifurcation Chaos , vol.13 , pp. 2935-2948
    • di Bernardo, M.1    Kowalczyk, P.2    Nordmark, A.3
  • 26
    • 34547669762 scopus 로고    scopus 로고
    • Filippov, A.F., 1964. Differential equations with discontinuous right-hand side. In: American Mathematical Society Translations, Series 2. AMS, Ann Arbor, pp. 199-231.
  • 28
    • 0032428822 scopus 로고    scopus 로고
    • Limitations of low-intensity selective logging for sustainable tropical forestry
    • Fredericksen T.S. Limitations of low-intensity selective logging for sustainable tropical forestry. Commun. For. Rev. 77 (1998) 262-266
    • (1998) Commun. For. Rev. , vol.77 , pp. 262-266
    • Fredericksen, T.S.1
  • 29
    • 0027706230 scopus 로고
    • Invasion and chaos in a periodically pulsed mass-action chemostat
    • Funasaki E., and Kot M. Invasion and chaos in a periodically pulsed mass-action chemostat. Theor. Popul. Biol. 44 (1993) 203-224
    • (1993) Theor. Popul. Biol. , vol.44 , pp. 203-224
    • Funasaki, E.1    Kot, M.2
  • 31
    • 0033594935 scopus 로고    scopus 로고
    • Unpalatable prey resolves the paradox of enrichment
    • Genkai-Kato M., and Yamamura N. Unpalatable prey resolves the paradox of enrichment. Proc. R. Soc. London B. 266 (1999) 1215-1219
    • (1999) Proc. R. Soc. London B. , vol.266 , pp. 1215-1219
    • Genkai-Kato, M.1    Yamamura, N.2
  • 32
    • 1942421278 scopus 로고    scopus 로고
    • On the mechanistic underpinning of discrete-time population models with complex dynamics
    • Geritz S.A.H., and Kisdi E. On the mechanistic underpinning of discrete-time population models with complex dynamics. J. Theor. Biol. 228 (2004) 261-269
    • (2004) J. Theor. Biol. , vol.228 , pp. 261-269
    • Geritz, S.A.H.1    Kisdi, E.2
  • 36
    • 0000843153 scopus 로고
    • A contribution to the theory of competing predators
    • Hsu S.B., Hubbel S.P., and Waltman P. A contribution to the theory of competing predators. Ecol. Monogr. 48 (1978) 337-349
    • (1978) Ecol. Monogr. , vol.48 , pp. 337-349
    • Hsu, S.B.1    Hubbel, S.P.2    Waltman, P.3
  • 37
    • 0034508738 scopus 로고    scopus 로고
    • Periodic mortality events in predator-prey systems
    • Ives A.R., Gross K., and Jansen V.A.A. Periodic mortality events in predator-prey systems. Ecology 81 (2000) 3330-3340
    • (2000) Ecology , vol.81 , pp. 3330-3340
    • Ives, A.R.1    Gross, K.2    Jansen, V.A.A.3
  • 38
    • 0030174263 scopus 로고    scopus 로고
    • Optimal foraging and predator-prey dynamics
    • Křivan V. Optimal foraging and predator-prey dynamics. Theor. Popul. Biol. 49 (1996) 265-290
    • (1996) Theor. Popul. Biol. , vol.49 , pp. 265-290
    • Křivan, V.1
  • 39
    • 0344269355 scopus 로고    scopus 로고
    • Dynamical consequences of optimal host feeding on host-parasitoid population dynamics
    • Křivan V. Dynamical consequences of optimal host feeding on host-parasitoid population dynamics. Bull. Math. Biol. 59 5 (1997) 809-831
    • (1997) Bull. Math. Biol. , vol.59 , Issue.5 , pp. 809-831
    • Křivan, V.1
  • 40
    • 0030619653 scopus 로고    scopus 로고
    • Dynamic ideal free distribution: effects of optimal path choice on predator-prey dynamics
    • Křivan V. Dynamic ideal free distribution: effects of optimal path choice on predator-prey dynamics. Am. Nat. 149 1 (1997) 164-178
    • (1997) Am. Nat. , vol.149 , Issue.1 , pp. 164-178
    • Křivan, V.1
  • 41
    • 0345487003 scopus 로고    scopus 로고
    • Effects of optimal antipredator behaviour of prey on predator-prey dynamics: the role of refuges
    • Křivan V. Effects of optimal antipredator behaviour of prey on predator-prey dynamics: the role of refuges. Theor. Popul. Biol. 53 (1998) 131-142
    • (1998) Theor. Popul. Biol. , vol.53 , pp. 131-142
    • Křivan, V.1
  • 42
    • 2542500093 scopus 로고    scopus 로고
    • Competitive co-existence caused by adaptive predators
    • Křivan V. Competitive co-existence caused by adaptive predators. Evol. Ecol. Res. 5 (2003) 1163-1182
    • (2003) Evol. Ecol. Res. , vol.5 , pp. 1163-1182
    • Křivan, V.1
  • 43
    • 13744263429 scopus 로고    scopus 로고
    • Adaptive omnivory and species coexistence in tri-trophic food webs
    • Křivan V., and Diehl S. Adaptive omnivory and species coexistence in tri-trophic food webs. Theor. Popul. Biol. 67 (2005) 85-99
    • (2005) Theor. Popul. Biol. , vol.67 , pp. 85-99
    • Křivan, V.1    Diehl, S.2
  • 44
    • 0141656321 scopus 로고    scopus 로고
    • Optimal foraging and predator-prey dynamics, III
    • Křivan V., and Eisner J. Optimal foraging and predator-prey dynamics, III. Theor. Popul. Biol. 63 (2003) 269-279
    • (2003) Theor. Popul. Biol. , vol.63 , pp. 269-279
    • Křivan, V.1    Eisner, J.2
  • 45
    • 1342330189 scopus 로고    scopus 로고
    • Adaptive foraging and flexible food web topology
    • Křivan V., and Schmitz O.J. Adaptive foraging and flexible food web topology. Evol. Ecol. Res. 5 (2003) 623-652
    • (2003) Evol. Ecol. Res. , vol.5 , pp. 623-652
    • Křivan, V.1    Schmitz, O.J.2
  • 46
    • 0038614850 scopus 로고    scopus 로고
    • Optimal foraging and predator-prey dynamics, II
    • Křivan V., and Sikder A. Optimal foraging and predator-prey dynamics, II. Theor. Popul. Biol. 55 (1999) 111-126
    • (1999) Theor. Popul. Biol. , vol.55 , pp. 111-126
    • Křivan, V.1    Sikder, A.2
  • 47
    • 0343924496 scopus 로고    scopus 로고
    • Searching for food or hosts: the influence of parasitoids behaviour on host-parasitoid dynamics
    • Křivan V., and Sirot E. Searching for food or hosts: the influence of parasitoids behaviour on host-parasitoid dynamics. Theor. Popul. Biol. 51 (1997) 201-209
    • (1997) Theor. Popul. Biol. , vol.51 , pp. 201-209
    • Křivan, V.1    Sirot, E.2
  • 49
    • 0029663443 scopus 로고    scopus 로고
    • Remarks on food chain dynamics
    • Kuznetsov Yu.A., and Rinaldi S. Remarks on food chain dynamics. Math. Biosci. 134 (1996) 1-33
    • (1996) Math. Biosci. , vol.134 , pp. 1-33
    • Kuznetsov, Yu.A.1    Rinaldi, S.2
  • 50
    • 0010427610 scopus 로고
    • Homoclinic bifurcations in slow-fast second order systems
    • Kuznetsov Yu.A., Muratori S., and Rinaldi S. Homoclinic bifurcations in slow-fast second order systems. Nonlinear Anal. 25 (1995) 747-762
    • (1995) Nonlinear Anal. , vol.25 , pp. 747-762
    • Kuznetsov, Yu.A.1    Muratori, S.2    Rinaldi, S.3
  • 51
    • 0036252851 scopus 로고    scopus 로고
    • Belyakov homoclinic bifurcations in a tritrophic food chain model
    • Kuznetsov Yu.A., de Feo O., and Rinaldi S. Belyakov homoclinic bifurcations in a tritrophic food chain model. SIAM J. Appl. Math. 62 2 (2001) 462-487
    • (2001) SIAM J. Appl. Math. , vol.62 , Issue.2 , pp. 462-487
    • Kuznetsov, Yu.A.1    de Feo, O.2    Rinaldi, S.3
  • 52
  • 53
    • 0042834359 scopus 로고    scopus 로고
    • Nonlinear mathematical model of pulsed therapy of heterogeneous tumors
    • Lakmeche A., and Arino O. Nonlinear mathematical model of pulsed therapy of heterogeneous tumors. Nonlinear Anal. R. World Appl. 2 (2001) 455-465
    • (2001) Nonlinear Anal. R. World Appl. , vol.2 , pp. 455-465
    • Lakmeche, A.1    Arino, O.2
  • 54
    • 0037332898 scopus 로고    scopus 로고
    • Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator
    • Liu X., and Chen L. Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator. Chaos Solitons Fractals 16 2 (2003) 311-320
    • (2003) Chaos Solitons Fractals , vol.16 , Issue.2 , pp. 311-320
    • Liu, X.1    Chen, L.2
  • 55
    • 33746536797 scopus 로고    scopus 로고
    • A second-order impact model for forest fire regimes
    • Maggi S., and Rinaldi S. A second-order impact model for forest fire regimes. Theor. Popul. Biol. 70 (2006) 174-182
    • (2006) Theor. Popul. Biol. , vol.70 , pp. 174-182
    • Maggi, S.1    Rinaldi, S.2
  • 56
    • 0039645998 scopus 로고
    • Limit cycles in predator-prey communities
    • May R.M. Limit cycles in predator-prey communities. Science 177 (1972) 900-902
    • (1972) Science , vol.177 , pp. 900-902
    • May, R.M.1
  • 57
    • 0029479690 scopus 로고
    • Bifurcation structure of a three-species food-chain model
    • McCann K., and Yodzis P. Bifurcation structure of a three-species food-chain model. Theor. Popul. Biol. 48 (1995) 93-125
    • (1995) Theor. Popul. Biol. , vol.48 , pp. 93-125
    • McCann, K.1    Yodzis, P.2
  • 58
    • 18844421334 scopus 로고    scopus 로고
    • Threshold policies control for predator-prey systems using a control Liapunov function approach
    • Meza M.E.M., Bhaya A., Kaszkurewicz E., and da Silveira Costa M.I. Threshold policies control for predator-prey systems using a control Liapunov function approach. Theor. Popul. Biol. 67 (2005) 273-284
    • (2005) Theor. Popul. Biol. , vol.67 , pp. 273-284
    • Meza, M.E.M.1    Bhaya, A.2    Kaszkurewicz, E.3    da Silveira Costa, M.I.4
  • 59
    • 4143063877 scopus 로고    scopus 로고
    • Analysis of periodic growth disturbance models
    • Reluga T.C. Analysis of periodic growth disturbance models. Theor. Popul. Biol. 66 (2004) 151-161
    • (2004) Theor. Popul. Biol. , vol.66 , pp. 151-161
    • Reluga, T.C.1
  • 60
    • 0001524523 scopus 로고
    • Graphical representation and stability conditions of predator-prey interaction
    • Rosenzweig M.P., and MacArthur R.H. Graphical representation and stability conditions of predator-prey interaction. Am. Nat. 97 (1963) 209-223
    • (1963) Am. Nat. , vol.97 , pp. 209-223
    • Rosenzweig, M.P.1    MacArthur, R.H.2
  • 61
    • 33645130338 scopus 로고    scopus 로고
    • Dancing between the devil and deep blue sea: the stabilizing effect of enemy-free and victimless sinks
    • Schreiber S.J., Lipcius R.N., Seitz R.D., and Long W.C. Dancing between the devil and deep blue sea: the stabilizing effect of enemy-free and victimless sinks. Oikos 113 (2006) 67-81
    • (2006) Oikos , vol.113 , pp. 67-81
    • Schreiber, S.J.1    Lipcius, R.N.2    Seitz, R.D.3    Long, W.C.4
  • 62
    • 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) 1-26
    • (1998) Bull. Math. Biol. , vol.60 , pp. 1-26
    • Shulgin, B.1    Stone, L.2    Agur, Z.3
  • 63
    • 18844475269 scopus 로고    scopus 로고
    • Adaptive superparasitism and host-parasitoid dynamics
    • Sirot E., and Křivan V. Adaptive superparasitism and host-parasitoid dynamics. Bull. Math. Biol. 59 1 (1997) 23-41
    • (1997) Bull. Math. Biol. , vol.59 , Issue.1 , pp. 23-41
    • Sirot, E.1    Křivan, V.2
  • 64
    • 7444228735 scopus 로고    scopus 로고
    • Influence of prey reserve capacity on predator-prey dynamics
    • Srinivasu P.D.N., and Gayatri I.L. Influence of prey reserve capacity on predator-prey dynamics. Ecol. Model. 181 (2005) 191-202
    • (2005) Ecol. Model. , vol.181 , pp. 191-202
    • Srinivasu, P.D.N.1    Gayatri, I.L.2
  • 65
    • 0004287950 scopus 로고
    • Princeton University Press, Princeton, NJ, USA
    • Stephens D.W., and Krebs J.R. Foraging Theory (1986), Princeton University Press, Princeton, NJ, USA
    • (1986) Foraging Theory
    • Stephens, D.W.1    Krebs, J.R.2
  • 66
    • 0035007927 scopus 로고    scopus 로고
    • Alternative food, switching predators, and the persistence of predator-prey systems
    • Van Baalen M., Křivan V., Van Rijn P.C.J., and Sabelis M.W. Alternative food, switching predators, and the persistence of predator-prey systems. Am. Nat. 157 5 (2001) 512-524
    • (2001) Am. Nat. , vol.157 , Issue.5 , pp. 512-524
    • Van Baalen, M.1    Křivan, V.2    Van Rijn, P.C.J.3    Sabelis, M.W.4
  • 67
    • 0025331493 scopus 로고
    • Limit cycles in predator-prey models
    • Wrzosek D.M. Limit cycles in predator-prey models. Math. Biosci. 98 (1990) 1-12
    • (1990) Math. Biosci. , vol.98 , pp. 1-12
    • Wrzosek, D.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.