메뉴 건너뛰기




Volumn 17, Issue 8, 2015, Pages

Conditional random matrix ensembles and the stability of dynamical systems

Author keywords

control; dynamical systems; stability

Indexed keywords

COMPLEX NETWORKS; CONTROL; CONVERGENCE OF NUMERICAL METHODS; DYNAMICAL SYSTEMS; JACOBIAN MATRICES; RANDOM VARIABLES; STABILITY;

EID: 84941584965     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/17/8/083025     Document Type: Article
Times cited : (15)

References (45)
  • 1
    • 19444371087 scopus 로고    scopus 로고
    • Will a large complex system with time delays be stable?
    • Jirsa V and Ding M 2004 Will a large complex system with time delays be stable? Phys. Rev. Lett. 93 070602
    • (2004) Phys. Rev. Lett. , vol.93
    • Jirsa, V.1    Ding, M.2
  • 2
    • 33645766195 scopus 로고    scopus 로고
    • Speed of synchronization in complex networks of neural oscillators: Analytic results based on random matrix theory
    • Timme M, Geisel T and Wolf F 2006 Speed of synchronization in complex networks of neural oscillators: analytic results based on random matrix theory Chaos 16 015108
    • (2006) Chaos , vol.16
    • Timme, M.1    Geisel, T.2    Wolf, F.3
  • 3
    • 84866903962 scopus 로고    scopus 로고
    • How synaptic weights determine stability of synchrony in networks of pulse-coupled excitatory and inhibitory oscillators
    • Kriener B 2012 How synaptic weights determine stability of synchrony in networks of pulse-coupled excitatory and inhibitory oscillators Chaos 22 033143
    • (2012) Chaos , vol.22
    • Kriener, B.1
  • 4
    • 85032751496 scopus 로고    scopus 로고
    • Signal processing in large systems: A new paradigm
    • Couillet R and Debbah M 2013 Signal processing in large systems: a new paradigm IEEE Signal Process. Mag. 30 24-39
    • (2013) IEEE Signal Process. Mag. , vol.30 , pp. 24-39
    • Couillet, R.1    Debbah, M.2
  • 5
    • 0015514970 scopus 로고
    • Will a large complex system be stable?
    • May R M 1972 Will a large complex system be stable? Nature 238 413-4
    • (1972) Nature , vol.238 , pp. 413-414
    • May, R.M.1
  • 6
    • 0034636310 scopus 로고    scopus 로고
    • The diversity-stability debate
    • McCann K S 2000 The diversity-stability debate Nature 405 228-33
    • (2000) Nature , vol.405 , pp. 228-233
    • McCann, K.S.1
  • 7
    • 78751671623 scopus 로고    scopus 로고
    • Systemic risk in banking ecosystems
    • Haldane A G and May R M 2011 Systemic risk in banking ecosystems Nature 469 351-5
    • (2011) Nature , vol.469 , pp. 351-355
    • Haldane, A.G.1    May, R.M.2
  • 8
    • 33645684557 scopus 로고    scopus 로고
    • Synchronization in networks with random interactions: Theory and applications
    • Feng J, Jirsa V K and Ding M 2006 Synchronization in networks with random interactions: theory and applications Chaos: Interdiscip. J. Nonlinear Sci. 16 015109
    • (2006) Chaos: Interdiscip. J. Nonlinear Sci. , vol.16
    • Feng, J.1    Jirsa, V.K.2    Ding, M.3
  • 13
    • 0001372773 scopus 로고
    • Fluctuations of animal populations and a measure of community stability
    • MacArthur R 1955 Fluctuations of animal populations and a measure of community stability Ecology 36 533
    • (1955) Ecology , vol.36 , pp. 533
    • MacArthur, R.1
  • 14
    • 36949041214 scopus 로고
    • Connectance of large dynamic (cybernetic) systems: Critical values for stability
    • Gardner M R and Ashby W R 1970 Connectance of large dynamic (cybernetic) systems: critical values for stability Nature 228 784
    • (1970) Nature , vol.228 , pp. 784
    • Gardner, M.R.1    Ashby, W.R.2
  • 16
    • 19844372999 scopus 로고    scopus 로고
    • Random matrix theory
    • Edelman A and Rao N R 1999 Random matrix theory Acta Numer. 14 233-97
    • (1999) Acta Numer. , vol.14 , pp. 233-297
    • Edelman, A.1    Rao, N.R.2
  • 18
    • 77957124985 scopus 로고    scopus 로고
    • Random matrices: Universality of esds and the circular law
    • Tao T, Vu V and Krishnapur M 2010 Random matrices: universality of esds and the circular law Ann. Probab. 38 2023-65
    • (2010) Ann. Probab. , vol.38 , pp. 2023-2065
    • Tao, T.1    Vu, V.2    Krishnapur, M.3
  • 19
    • 0033850249 scopus 로고    scopus 로고
    • Maximally stable model ecosystems can be highly connected
    • Haydon D T 2000 Maximally stable model ecosystems can be highly connected Ecology 81 2631-6
    • (2000) Ecology , vol.81 , pp. 2631-2636
    • Haydon, D.T.1
  • 20
    • 0037052507 scopus 로고    scopus 로고
    • Stability in real food webs: Weak links in long loops
    • Neutel A M 2002 Stability in real food webs: weak links in long loops Science 296 1120-3
    • (2002) Science , vol.296 , pp. 1120-1123
    • Neutel, A.M.1
  • 21
    • 84857994997 scopus 로고    scopus 로고
    • Stability criteria for complex ecosystems
    • Allesina S and Tang S 2012 Stability criteria for complex ecosystems Nature 483 205-8
    • (2012) Nature , vol.483 , pp. 205-208
    • Allesina, S.1    Tang, S.2
  • 22
    • 0003620050 scopus 로고
    • A comment on randomly constructed model ecosystems
    • Lawlor L R 1978 A comment on randomly constructed model ecosystems Am. Nat. 112 445-7
    • (1978) Am. Nat. , vol.112 , pp. 445-447
    • Lawlor, L.R.1
  • 23
    • 0028181948 scopus 로고
    • Biodiversity and stability in grasslands
    • Tilman D and Downing J A 1994 Biodiversity and stability in grasslands Nature 367 363-5
    • (1994) Nature , vol.367 , pp. 363-365
    • Tilman, D.1    Downing, J.A.2
  • 24
    • 0028129196 scopus 로고
    • Does diversity beget stability?
    • Givnish T J 1994 Does diversity beget stability? Nature 371 113-4
    • (1994) Nature , vol.371 , pp. 113-114
    • Givnish, T.J.1
  • 25
    • 0016355099 scopus 로고
    • The stability of a feasible random ecosystem
    • Roberts A 1974 The stability of a feasible random ecosystem Nature 251 607-8
    • (1974) Nature , vol.251 , pp. 607-608
    • Roberts, A.1
  • 26
    • 0000693355 scopus 로고
    • Stability of feasible predator-prey systems
    • Gilpin M E 1975 Stability of feasible predator-prey systems Nature 254 137-9
    • (1975) Nature , vol.254 , pp. 137-139
    • Gilpin, M.E.1
  • 27
    • 0021036658 scopus 로고
    • Complexity, diversity, and stability - A reconciliation of theoretical and empirical results
    • King A W and Pimm S L 1983 Complexity, diversity, and stability - a reconciliation of theoretical and empirical results Am. Nat. 122 229-39
    • (1983) Am. Nat. , vol.122 , pp. 229-239
    • King, A.W.1    Pimm, S.L.2
  • 28
    • 0021607939 scopus 로고
    • The complexity and stability of ecosystems
    • Pimm S 1984 The complexity and stability of ecosystems Nature 307 321-6
    • (1984) Nature , vol.307 , pp. 321-326
    • Pimm, S.1
  • 29
    • 0032558786 scopus 로고    scopus 로고
    • Weak trophic interactions and the balance of nature
    • McCann K, Hastings A and Huxel G R 1998 Weak trophic interactions and the balance of nature Nature 395 794-8
    • (1998) Nature , vol.395 , pp. 794-798
    • McCann, K.1    Hastings, A.2    Huxel, G.R.3
  • 30
  • 31
    • 0038050538 scopus 로고    scopus 로고
    • Complexity and stability revisited
    • Jansen V A A and Kokkoris G D 2003 Complexity and stability revisited Ecol. Lett. 6 498-502
    • (2003) Ecol. Lett. , vol.6 , pp. 498-502
    • Jansen, V.A.A.1    Kokkoris, G.D.2
  • 32
    • 44749088923 scopus 로고    scopus 로고
    • Complexity does not affect stability in feasible model communities
    • Christianou M and Kokkoris G D 2008 Complexity does not affect stability in feasible model communities J. Theor. Biol. 253 162-9
    • (2008) J. Theor. Biol. , vol.253 , pp. 162-169
    • Christianou, M.1    Kokkoris, G.D.2
  • 33
    • 0003013212 scopus 로고
    • Statistical properties of real symmetric matrices with many dimensions
    • ed MacPhail M.S.
    • Wigner E P 1959 Statistical properties of real symmetric matrices with many dimensions Proc. 4th Canadian Mathematical Congress ed M S MacPhail (Toronto: University of Toronto Press) pp 174-84
    • (1959) Proc. 4th Canadian Mathematical Congress , pp. 174-184
    • Wigner, E.P.1
  • 34
    • 0242290678 scopus 로고    scopus 로고
    • Quantum chaos, irreversible classical dynamics, and random matrix theory
    • Andreev A V et al 1996 Quantum chaos, irreversible classical dynamics, and random matrix theory Phys. Rev. Lett. 76 3947-50
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 3947-3950
    • Andreev, A.V.1
  • 37
    • 84884351044 scopus 로고    scopus 로고
    • Do simple models lead to generality in ecology?
    • Evans M R et al 2013 Do simple models lead to generality in ecology? Trends Ecol. Evol. 28 578-83
    • (2013) Trends Ecol. Evol. , vol.28 , pp. 578-583
    • Evans, M.R.1
  • 38
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • Lorenz E N 1963 Deterministic nonperiodic flow J. Atmos. Sci. 20 130-48
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-148
    • Lorenz, E.N.1
  • 39
    • 0025826876 scopus 로고
    • Modeling the cell division cycle: Cdc2 and cyclin interactions
    • Tyson J J 1991 Modeling the cell division cycle: cdc2 and cyclin interactions Proc. Natl Acad. Sci. USA 88 7328-32
    • (1991) Proc. Natl Acad. Sci. USA , vol.88 , pp. 7328-7332
    • Tyson, J.J.1
  • 40
    • 0029985351 scopus 로고    scopus 로고
    • Population dynamics of immune responses to persistent viruses
    • Nowak M A and Bangham C 1996 Population dynamics of immune responses to persistent viruses Science, NY 272 74-79
    • (1996) Science, NY , vol.272 , pp. 74-79
    • Nowak, M.A.1    Bangham, C.2
  • 41
    • 0021690803 scopus 로고
    • Seasonality and period-doubling bifurcations in an epidemic model
    • Aron J L and Schwartz I B 1984 Seasonality and period-doubling bifurcations in an epidemic model J. Theor. Biol. 110 665-79
    • (1984) J. Theor. Biol. , vol.110 , pp. 665-679
    • Aron, J.L.1    Schwartz, I.B.2
  • 43
    • 84881526872 scopus 로고    scopus 로고
    • Approximate Bayesian computation (ABC) gives exact results under the assumption of model error
    • Wilkinson R D 2013 Approximate Bayesian computation (ABC) gives exact results under the assumption of model error Stat. Appl. Genet. Mol. Biol. 12 129-41
    • (2013) Stat. Appl. Genet. Mol. Biol. , vol.12 , pp. 129-141
    • Wilkinson, R.D.1
  • 44
    • 39149116715 scopus 로고    scopus 로고
    • Generating confidence intervals on biological networks
    • Thorne T W and Stumpf M P H 2007 Generating confidence intervals on biological networks BMC Bioinform. 8 467
    • (2007) BMC Bioinform. , vol.8 , pp. 467
    • Thorne, T.W.1    Stumpf, M.P.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.