메뉴 건너뛰기




Volumn 12, Issue 2, 2013, Pages 1031-1084

Dynamics of stochastically blinking systems. Part II: Asymptotic properties

Author keywords

Attractor; Averaging; Blinking networks; Stochastic switching

Indexed keywords

ACTION FUNCTIONAL; ASYMPTOTIC PROPERTIES; ATTRACTOR; AVERAGING; LYAPUNOV FUNCTION METHOD; MULTIPLE ATTRACTORS; PROBABILITY THEORY; STOCHASTIC SWITCHING;

EID: 84882969584     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/120893410     Document Type: Article
Times cited : (62)

References (46)
  • 1
    • 0035826155 scopus 로고    scopus 로고
    • Exploring complex networks
    • S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), pp. 268-276.
    • (2001) Nature , vol.410 , pp. 268-276
    • Strogatz, S.H.1
  • 2
    • 0038483826 scopus 로고    scopus 로고
    • Emergence of scaling in random networks
    • A. L. Barabasi and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), pp. 509- 512.
    • (1999) Science , vol.286 , pp. 509-512
    • Barabasi, A.L.1    Albert, R.2
  • 3
    • 0038718854 scopus 로고    scopus 로고
    • The structure and function of complex networks
    • M. E. J. Newman, The structure and function of complex networks, SIAM Rev., 45 (2003), pp. 167-256.
    • (2003) SIAM Rev. , vol.45 , pp. 167-256
    • Newman, M.E.J.1
  • 4
    • 4243241129 scopus 로고    scopus 로고
    • Master stability function for synchronized coupled systems
    • L. M. Pecora and T. L. Carroll, Master stability function for synchronized coupled systems, Phys. Rev. Lett., 80 (1998), pp. 2109-2112.
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 2109-2112
    • Pecora, L.M.1    Carroll, T.L.2
  • 5
    • 3042858242 scopus 로고    scopus 로고
    • Connection graph stability method for synchronized coupled chaotic systems
    • V. Belykh, I. Belykh, and M. Hasler, Connection graph stability method for synchronized coupled chaotic systems, Phys. D, 195 (2004), pp. 159-187.
    • (2004) Phys. D , vol.195 , pp. 159-187
    • Belykh, V.1    Belykh, I.2    Hasler, M.3
  • 6
    • 33750999583 scopus 로고    scopus 로고
    • Generalized connection graph method for synchronization in asymmetrical networks
    • I. Belykh, V. Belykh, and M. Hasler, Generalized connection graph method for synchronization in asymmetrical networks, Phys. D, 224 (2006), pp. 42-51.
    • (2006) Phys. D , vol.224 , pp. 42-51
    • Belykh, I.1    Belykh, V.2    Hasler, M.3
  • 11
    • 3042776965 scopus 로고    scopus 로고
    • Blinking model and synchronization in small-world networks with a time-varying coupling
    • I. Belykh, V. Belykh, and M. Hasler, Blinking model and synchronization in small-world networks with a time-varying coupling, Phys. D, 195 (2004), pp. 188-206.
    • (2004) Phys. D , vol.195 , pp. 188-206
    • Belykh, I.1    Belykh, V.2    Hasler, M.3
  • 12
    • 27844486130 scopus 로고    scopus 로고
    • Blinking long-range connections increase the functionality of locally connected networks
    • M. Hasler and I. Belykh, Blinking long-range connections increase the functionality of locally connected networks, IEICE Trans. Fund., E88-A (2005), pp. 2647-2655.
    • (2005) IEICE Trans. Fund. , vol.E88-A , pp. 2647-2655
    • Hasler, M.1    Belykh, I.2
  • 13
    • 23944438241 scopus 로고    scopus 로고
    • Communication and synchronization in disconnected networks with dynamic topology: Moving neighborhood networks
    • J. D. Skufca and E. M. Bollt, Communication and synchronization in disconnected networks with dynamic topology: Moving neighborhood networks, Math. Biosci. Eng., 1 (2004), pp. 347-359.
    • (2004) Math. Biosci. Eng. , vol.1 , pp. 347-359
    • Skufca, J.D.1    Bollt, E.M.2
  • 14
    • 33751011310 scopus 로고    scopus 로고
    • Random talk: Random walk and synchronizability in a moving neighborhood network
    • M. Porfiri, D. J. Stilwell, E. M. Bollt, and J. D. Skufca, Random talk: Random walk and synchronizability in a moving neighborhood network, Phys. D, 224 (2006), pp. 102-113.
    • (2006) Phys. D , vol.224 , pp. 102-113
    • Porfiri, M.1    Stilwell, D.J.2    Bollt, E.M.3    Skufca, J.D.4
  • 15
    • 55849087550 scopus 로고    scopus 로고
    • Master-slave global stochastic synchronization of chaotic oscillators
    • M. Porfiri and R. Pigliacampo, Master-slave global stochastic synchronization of chaotic oscillators, SIAM J. Appl. Dyn. Syst., 7 (2008), pp. 825-842.
    • (2008) SIAM J. Appl. Dyn. Syst. , vol.7 , pp. 825-842
    • Porfiri, M.1    Pigliacampo, R.2
  • 16
    • 77953086882 scopus 로고    scopus 로고
    • Evolving enhanced topologies for the synchronization of dynamical complex networks
    • T. Gorochowski, M. Di Bernardo, and C. Groerson, Evolving enhanced topologies for the synchronization of dynamical complex networks, Phys. Rev. E (3), 81 (2010), 056212.
    • (2010) Phys. Rev. e , vol.81 , Issue.3 , pp. 12
    • Gorochowski, T.1    Di Bernardo, M.2    Groerson, C.3
  • 18
    • 41449083290 scopus 로고    scopus 로고
    • Adaptive synchronization of dynamics on evolving complex networks
    • F. Sorrentino and E. Ott, Adaptive synchronization of dynamics on evolving complex networks, Phys. Rev. Lett., 100 (2008), 114101.
    • (2008) Phys. Rev. Lett. , vol.100 , pp. 01
    • Sorrentino, F.1    Ott, E.2
  • 19
    • 54749087525 scopus 로고    scopus 로고
    • Synchronization in interacting populations of heterogeneous oscillators with time-varying coupling
    • P. So, B. Cotton, and E. Barreto, Synchronization in interacting populations of heterogeneous oscillators with time-varying coupling, Chaos, 18 (2008), 037114.
    • (2008) Chaos , vol.18 , pp. 14
    • So, P.1    Cotton, B.2    Barreto, E.3
  • 20
    • 80053404723 scopus 로고    scopus 로고
    • Generating macroscopic chaos in a network of globally coupled phase oscillators
    • P. So and E. Barreto, Generating macroscopic chaos in a network of globally coupled phase oscillators, Chaos, 21 (2011), 033127.
    • (2011) Chaos , vol.21 , pp. 27
    • So, P.1    Barreto, E.2
  • 21
    • 84882997961 scopus 로고    scopus 로고
    • Dynamics of stochastically blinking systems. Part I: Finite time properties
    • M. Hasler, V. Belykh, and I. Belykh, Dynamics of stochastically blinking systems. Part I: Finite time properties, SIAM J. Appl. Dyn. Syst., 12 (2013), pp. 1007-1030.
    • (2013) SIAM J. Appl. Dyn. Syst. , vol.12 , pp. 1007-1030
    • Hasler, M.1    Belykh, V.2    Belykh, I.3
  • 22
    • 0037520372 scopus 로고    scopus 로고
    • Complex behavior in switching power converters
    • C. Tse and M. Di Bernardo, Complex behavior in switching power converters, Proc. IEEE, 90 (2002), pp. 768-781.
    • (2002) Proc. IEEE , vol.90 , pp. 768-781
    • Tse, C.1    Di Bernardo, M.2
  • 23
    • 0009556713 scopus 로고    scopus 로고
    • Randomized modulation in power electronic converters
    • A. Stankovic and H. Lev-Ari, Randomized modulation in power electronic converters, Proc. IEEE, 90 (2002), pp. 782-799.
    • (2002) Proc. IEEE , vol.90 , pp. 782-799
    • Stankovic, A.1    Lev-Ari, H.2
  • 25
    • 0027556272 scopus 로고
    • Winner-take-all cellular neural network
    • G. Seiler and J. Nossek, Winner-take-all cellular neural network, IEEE Trans. Circuits Syst. II, 40 (1993), pp. 184-190.
    • (1993) IEEE Trans. Circuits Syst. II , vol.40 , pp. 184-190
    • Seiler, G.1    Nossek, J.2
  • 26
    • 84882999900 scopus 로고
    • Albert Blanchard ed., Paris
    • J.-L. Lagrange, Mecanique Analytique, Vols. I and II, Albert Blanchard ed., Paris, 1788.
    • (1788) Mecanique Analytique , vol.1-2
    • Lagrange, J.-L.1
  • 32
    • 0039735665 scopus 로고
    • Ergodic properties of a kicked damped particle
    • C. Beck, Ergodic properties of a kicked damped particle, Comm. Math. Phys., 130 (1990), pp. 51-60.
    • (1990) Comm. Math. Phys. , vol.130 , pp. 51-60
    • Beck, C.1
  • 34
    • 0000828252 scopus 로고
    • Diffusion processes on graphs and the averaging principle
    • M. I. Freidlin and A. D. Wentzell, Diffusion processes on graphs and the averaging principle, Ann. Probab., 21 (1993), pp. 2215-2245.
    • (1993) Ann. Probab. , vol.21 , pp. 2215-2245
    • Freidlin, M.I.1    Wentzell, A.D.2
  • 36
    • 84856284524 scopus 로고    scopus 로고
    • Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging
    • Yu. Kifer, Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging, Mem. Amer. Math. Soc., 201 (2009), 944.
    • (2009) Mem. Amer. Math. Soc. , vol.201
    • Kifer, Yu.1
  • 37
    • 0001761644 scopus 로고
    • A limit theorem for the solutions of differential equations with random right-hand sides
    • R. Z. Khas'minskii, A limit theorem for the solutions of differential equations with random right-hand sides, Theory Probab. Appl., 11 (1966), pp. 390-406.
    • (1966) Theory Probab. Appl. , vol.11 , pp. 390-406
    • Khas'minskii, R.Z.1
  • 38
    • 0003998877 scopus 로고
    • 4th ed., Springer-Verlag, New York, Heidelberg
    • M. Loeve, Probability Theory 1, 4th ed., Springer-Verlag, New York, Heidelberg, 1977.
    • (1977) Probability Theory 1
    • Loeve, M.1
  • 39
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc., 58 (1963), pp. 13-30.
    • (1963) J. Amer. Statist. Assoc. , vol.58 , pp. 13-30
    • Hoeffding, W.1
  • 40
    • 84882987935 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • B. Victor, Aspects of Combinatorics, Cambridge University Press, Cambridge, UK, 1993.
    • (1993) Aspects of Combinatorics
    • Victor, B.1
  • 42
    • 0034853039 scopus 로고    scopus 로고
    • Input-to-state stability for nonlinear time-varying systems via averaging
    • D. Nesic and A. R. Teel, Input-to-state stability for nonlinear time-varying systems via averaging, Math. Control Signals Systems, 14 (2001), pp. 257-280.
    • (2001) Math. Control Signals Systems , vol.14 , pp. 257-280
    • Nesic, D.1    Teel, A.R.2
  • 43
    • 0033148910 scopus 로고    scopus 로고
    • Exponential stability of nonlinear time-varying systems
    • D. Ayels and J. Peuteman, Exponential stability of nonlinear time-varying systems, Automatica, 35 (1999), pp. 1091-1100.
    • (1999) Automatica , vol.35 , pp. 1091-1100
    • Ayels, D.1    Peuteman, J.2
  • 45
    • 84866342427 scopus 로고    scopus 로고
    • Invariant densities for dynamical systems with random switching
    • Y. Bakhtin and T. Hurth, Invariant densities for dynamical systems with random switching, Nonlinearity, 25 (2012), pp. 2937-2952.
    • (2012) Nonlinearity , vol.25 , pp. 2937-2952
    • Bakhtin, Y.1    Hurth, T.2
  • 46
    • 64549122144 scopus 로고    scopus 로고
    • Explicit invariant measures for products of random matrices
    • J. Marklof, Y. Tourigny, and L. Wolowski, Explicit invariant measures for products of random matrices, Trans. Amer. Math. Soc., 360 (2008), pp. 3391-3427.
    • (2008) Trans. Amer. Math. Soc. , vol.360 , pp. 3391-3427
    • Marklof, J.1    Tourigny, Y.2    Wolowski, L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.