메뉴 건너뛰기




Volumn 6, Issue 1, 2006, Pages 1-21

Attractors for stochastic lattice dynamical systems

Author keywords

Random attractors; Stochastic lattice differential equations

Indexed keywords


EID: 33746270475     PISSN: 02194937     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219493706001621     Document Type: Article
Times cited : (293)

References (41)
  • 1
    • 21844518397 scopus 로고
    • Chaos of traveling waves in a discrete chain of diffusively coupled maps
    • V. S. Afraimovich and V. I. Nekorkin, Chaos of traveling waves in a discrete chain of diffusively coupled maps, Int. J. Bifur. Chaos. 4 (1994) 631-637.
    • (1994) Int. J. Bifur. Chaos. , vol.4 , pp. 631-637
    • Afraimovich, V.S.1    Nekorkin, V.I.2
  • 3
    • 21844488246 scopus 로고
    • Perfect cocycles through stochastic differential equations
    • L. Arnold and M. Scheutzow, Perfect cocycles through stochastic differential equations, Probab. Th. Rel. Fields 101 (1995) 65-88.
    • (1995) Probab. Th. Rel. Fields , vol.101 , pp. 65-88
    • Arnold, L.1    Scheutzow, M.2
  • 4
    • 0033268806 scopus 로고    scopus 로고
    • A discrete convolution model for phase transitions
    • P. W. Bates and A. Chmaj, A discrete convolution model for phase transitions, Arch. Rat. Mech. Anal. 150 (1999) 281-305.
    • (1999) Arch. Rat. Mech. Anal. , vol.150 , pp. 281-305
    • Bates, P.W.1    Chmaj, A.2
  • 5
    • 0035581833 scopus 로고    scopus 로고
    • Attractors for lattice dynamical systems
    • P. W. Bates, K. Lu and B. Wang, Attractors for lattice dynamical systems, Int. J. Bifur. Chaos 11 (2001) 143-153.
    • (2001) Int. J. Bifur. Chaos , vol.11 , pp. 143-153
    • Bates, P.W.1    Lu, K.2    Wang, B.3
  • 6
    • 0019582693 scopus 로고
    • Some threshhold results for models of myelinated nerves
    • J. Bell, Some threshhold results for models of myelinated nerves, Math. Biosci. 54 (1981) 181-190.
    • (1981) Math. Biosci. , vol.54 , pp. 181-190
    • Bell, J.1
  • 7
    • 0021408619 scopus 로고
    • Threshold behaviour and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons
    • J. Bell and C. Cosner, Threshold behaviour and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons, Quart. Appl. Math. 42 (1984) 1-14.
    • (1984) Quart. Appl. Math. , vol.42 , pp. 1-14
    • Bell, J.1    Cosner, C.2
  • 8
    • 0029390909 scopus 로고
    • Pattern formulation and spatial chaos in lattice dynamical systems: I
    • S.-N. Chow and J. Mallet-Paret, Pattern formulation and spatial chaos in lattice dynamical systems: I, IEEE Trans. Circuits Syst. 42 (1995) 746-751.
    • (1995) IEEE Trans. Circuits Syst. , vol.42 , pp. 746-751
    • Chow, S.-N.1    Mallet-Paret, J.2
  • 9
    • 0001379558 scopus 로고    scopus 로고
    • Traveling waves in lattice dynamical systems
    • S.-N. Chow, J. Mallet-Paret and W. Shen, Traveling waves in lattice dynamical systems, J. Diff. Eqns. 149 (1998) 248-291.
    • (1998) J. Diff. Eqns. , vol.149 , pp. 248-291
    • Chow, S.-N.1    Mallet-Paret, J.2    Shen, W.3
  • 10
    • 0000253503 scopus 로고    scopus 로고
    • Pattern formation and spatial chaos in spatially discrete evolution equations
    • S.-N. Chow, J. Mallet-Paret and E. S. Van Vleck, Pattern formation and spatial chaos in spatially discrete evolution equations, Random Comput. Dyn. 4 (1996) 109-178.
    • (1996) Random Comput. Dyn. , vol.4 , pp. 109-178
    • Chow, S.-N.1    Mallet-Paret, J.2    Van Vleck, E.S.3
  • 11
    • 0029545291 scopus 로고
    • Dynamics in a discrete Nagumo equation: Spatial topological chaos
    • S.-N. Chow and W. Shen, Dynamics in a discrete Nagumo equation: Spatial topological chaos, SIAM J. Appl. Math. 55 (1995) 1764-1781.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 1764-1781
    • Chow, S.-N.1    Shen, W.2
  • 13
    • 0024088955 scopus 로고
    • Cellular neural networks: Theory
    • L. O. Chua and L. Yang, Cellular neural networks: Theory, IEEE Trans. Circuits Syst. 35 (1988) 1257-1272.
    • (1988) IEEE Trans. Circuits Syst. , vol.35 , pp. 1257-1272
    • Chua, L.O.1    Yang, L.2
  • 14
    • 0024092072 scopus 로고
    • Cellular neural networks: Applications
    • L. O. Chua and L. Yang, Cellular neural networks: Applications, IEEE Trans. Circuits Syst. 35 (1988) 1273-1290.
    • (1988) IEEE Trans. Circuits Syst. , vol.35 , pp. 1273-1290
    • Chua, L.O.1    Yang, L.2
  • 16
    • 0035322004 scopus 로고    scopus 로고
    • Random point attractors versus random set attractors
    • H. Crauel, Random point attractors versus random set attractors, J. London Math. Soc. 63 (2002) 413-427.
    • (2002) J. London Math. Soc. , vol.63 , pp. 413-427
    • Crauel, H.1
  • 18
    • 21844482698 scopus 로고
    • Attractors for random dynamical systems
    • H. Crauel and F. Flandoli, Attractors for random dynamical systems, Probab. Th. Re. Fields 100 (1994) 365-393.
    • (1994) Probab. Th. Re. Fields , vol.100 , pp. 365-393
    • Crauel, H.1    Flandoli, F.2
  • 19
    • 0032008348 scopus 로고
    • Edge of chaos and local activity domain of Fitz-Hugh-Nagumo equation
    • R. Dogaru and L. O. Chua, Edge of chaos and local activity domain of Fitz-Hugh-Nagumo equation, Int. J. Bifur. Chaos 8 (1988) 211-257.
    • (1988) Int. J. Bifur. Chaos , vol.8 , pp. 211-257
    • Dogaru, R.1    Chua, L.O.2
  • 21
    • 43949163245 scopus 로고
    • Propagating waves in discrete bistable reaction diffusion systems
    • T. Erneux and G. Nicolis, Propagating waves in discrete bistable reaction diffusion systems, Physica D 67 (1993) 237-244.
    • (1993) Physica D , vol.67 , pp. 237-244
    • Erneux, T.1    Nicolis, G.2
  • 22
    • 8344235630 scopus 로고    scopus 로고
    • Stationary conjugation of flows for parabolic SPDEs with multiplicative noise and some applications
    • F. Flandoli and H. Lisei, Stationary conjugation of flows for parabolic SPDEs with multiplicative noise and some applications, Stoch. Anal. Appl. 22 (2004) 1385-1420.
    • (2004) Stoch. Anal. Appl. , vol.22 , pp. 1385-1420
    • Flandoli, F.1    Lisei, H.2
  • 23
    • 0001870021 scopus 로고    scopus 로고
    • Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative noise
    • F. Flandoli and B. Schmalfuß, Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative noise, Stoch. Stoch. Rep. 59 (1996) 21-45.
    • (1996) Stoch. Stoch. Rep. , vol.59 , pp. 21-45
    • Flandoli, F.1    Schmalfuß, B.2
  • 24
    • 0038415063 scopus 로고    scopus 로고
    • The conjugacy of stochastic and random differential equations and the existence of global attractors
    • P. Imkeller and B. Schmalfuß, The conjugacy of stochastic and random differential equations and the existence of global attractors, J. Dyn. Diff. Eqns. 13 (2001) 215-249.
    • (2001) J. Dyn. Diff. Eqns. , vol.13 , pp. 215-249
    • Imkeller, P.1    Schmalfuß, B.2
  • 25
    • 0000538108 scopus 로고
    • Discrete models for chemically reacting systems
    • R. Kapval, Discrete models for chemically reacting systems, J. Math. Chem. 6 (1991) 113-163.
    • (1991) J. Math. Chem. , vol.6 , pp. 113-163
    • Kapval, R.1
  • 27
    • 0023362335 scopus 로고
    • Propagation and its failure in coupled systems of discrete excitable cells
    • J. P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math. 47 (1987) 556-572.
    • (1987) SIAM J. Appl. Math. , vol.47 , pp. 556-572
    • Keener, J.P.1
  • 28
    • 0026035250 scopus 로고
    • The effects of discrete gap junction coupling on propagation in myocardium
    • J. P. Keener, The effects of discrete gap junction coupling on propagation in myocardium, J. Theor. Biol. 148 (1991) 49-82.
    • (1991) J. Theor. Biol. , vol.148 , pp. 49-82
    • Keener, J.P.1
  • 30
    • 0000234351 scopus 로고
    • Propagating failure in arrays of coupled bistable chemical reactors
    • J. P. Laplante and T. Erneux, Propagating failure in arrays of coupled bistable chemical reactors, J. Phys. Chem. 96 (1992) 4931-4934.
    • (1992) J. Phys. Chem. , vol.96 , pp. 4931-4934
    • Laplante, J.P.1    Erneux, T.2
  • 31
    • 0029390406 scopus 로고
    • Pattern formation and spatial chaos in lattice dynamical systems: II
    • J. Mallet-Paret and S.-N. Chow, Pattern formation and spatial chaos in lattice dynamical systems: II, IEEE Trans. Circuits Syst. 42 (1995) 752-756.
    • (1995) IEEE Trans. Circuits Syst. , vol.42 , pp. 752-756
    • Mallet-Paret, J.1    Chow, S.-N.2
  • 32
    • 53149083400 scopus 로고    scopus 로고
    • The global structure of traveling waves in spatially discrete dynamical systems
    • J. Mallet-Paret, The global structure of traveling waves in spatially discrete dynamical systems, J. Dyn. Diff. Eqns. 11 (1999) 49-127.
    • (1999) J. Dyn. Diff. Eqns. , vol.11 , pp. 49-127
    • Mallet-Paret, J.1
  • 36
    • 0002261964 scopus 로고
    • Characteristic exponents for a viscous fluid subjected to time dependent forces
    • D. Ruelle, Characteristic exponents for a viscous fluid subjected to time dependent forces, Comm. Math. Phys. 93 (1984) 285-300.
    • (1984) Comm. Math. Phys. , vol.93 , pp. 285-300
    • Ruelle, D.1
  • 37
    • 0036005048 scopus 로고    scopus 로고
    • Comparison of various concepts of a random attractor: A case study
    • M. Scheutzow, Comparison of various concepts of a random attractor: A case study, Arch. Math. 78 (2002) 233-240.
    • (2002) Arch. Math. , vol.78 , pp. 233-240
    • Scheutzow, M.1
  • 38
    • 51249193229 scopus 로고
    • Analysis of a myelinated nerve model
    • A. C. Scott, Analysis of a myelinated nerve model, Bull. Math. Biophys. 26 (1964) 247-254.
    • (1964) Bull. Math. Biophys. , vol.26 , pp. 247-254
    • Scott, A.C.1
  • 39
    • 0030269335 scopus 로고    scopus 로고
    • Lifted lattices, hyperbolic structures, and topological disorders in coupled map lattices
    • W. Shen, Lifted lattices, hyperbolic structures, and topological disorders in coupled map lattices, SIAM J. Appl. Math. 56 (1996) 1379-1399.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 1379-1399
    • Shen, W.1
  • 40
    • 0003678750 scopus 로고
    • Nonlinear Functional Analysis and its Applications. Vol. I: Fixed-Point Theorems
    • (Springer-Verlag)
    • E. Zeidler, Nonlinear Functional Analysis and its Applications. Vol. I: Fixed-Point Theorems (Springer-Verlag, 1986).
    • (1986)
    • Zeidler, E.1
  • 41
    • 0004711956 scopus 로고
    • Existence of traveling wavefront solutions for the discrete Nagumo equation
    • B. Zinner, Existence of traveling wavefront solutions for the discrete Nagumo equation, J. Diff. Eqns. 96 (1992) 1-27.
    • (1992) J. Diff. Eqns. , vol.96 , pp. 1-27
    • Zinner, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.