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Volumn 18, Issue 6, 2005, Pages 2827-2846

Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling

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EID: 26944444656     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/6/022     Document Type: Article
Times cited : (91)

References (31)
  • 1
    • 0028468031 scopus 로고
    • How delays affect neural dynamics and learning
    • Baldi P and Atiya A F 1994 How delays affect neural dynamics and learning IEEE Trans. Neural Networks 5 612-21
    • (1994) IEEE Trans. Neural Networks , vol.5 , Issue.4 , pp. 612-621
    • Baldi, P.1    Atiya, A.F.2
  • 2
    • 0028517922 scopus 로고
    • Stability and bifurcations of equilibria in a multiple-delayed differential equation
    • Bélair J and Campbell S A 1994 Stability and bifurcations of equilibria in a multiple-delayed differential equation SIAM J. Appl. Math. 54 1402-24
    • (1994) SIAM J. Appl. Math. , vol.54 , Issue.5 , pp. 1402-1424
    • Bélair, J.1    Campbell, S.A.2
  • 4
    • 0037457058 scopus 로고    scopus 로고
    • Restrictions and unfolding of double Hopf bifurcation in functional differential equations
    • Buono P and Bélair J 2003 Restrictions and unfolding of double Hopf bifurcation in functional differential equations J. Diff. Eqns 189 234-66
    • (2003) J. Diff. Eqns , vol.189 , Issue.1 , pp. 234-266
    • Buono, P.1    Bélair, J.2
  • 5
    • 0002848816 scopus 로고    scopus 로고
    • Stability and bifurcation of a simple neural network with multiple time delays
    • Campbell S A 1999 Stability and bifurcation of a simple neural network with multiple time delays Differential Equations with Application to Biology (Fields Institute Communications vol 21) ed S Ruan et al (Providence, RI: American Mathematical Society) pp 65-79
    • (1999) Differential Equations with Application to Biology , pp. 65-79
    • Campbell, S.A.1
  • 7
    • 0033177129 scopus 로고    scopus 로고
    • Qualitative analysis of a neural network model with multiple time delays
    • Campbell S A, Ruan S and Wei J 1999 Qualitative analysis of a neural network model with multiple time delays Int. J. Bifurcat. Chaos 9 1585-95
    • (1999) Int. J. Bifurcat. Chaos , vol.9 , Issue.8 , pp. 1585-1595
    • Campbell, S.A.1    Ruan, S.2    Wei, J.3
  • 8
    • 0020970741 scopus 로고
    • Absolute stability of global pattern formation and parallel memory storage by competitive neural networks
    • Cohen M and Grossberg S 1983 Absolute stability of global pattern formation and parallel memory storage by competitive neural networks IEEE Trans. Syst. Man Cybernet. 13 815-26
    • (1983) IEEE Trans. Syst. Man Cybernet. , vol.13 , pp. 815-826
    • Cohen, M.1    Grossberg, S.2
  • 9
    • 0000209631 scopus 로고
    • Discrete delay, distributed delay and stability switches
    • Cooke K L and Grossman Z 1982 Discrete delay, distributed delay and stability switches J. Math. Anal. Appl. 86 592-627
    • (1982) J. Math. Anal. Appl. , vol.86 , Issue.2 , pp. 592-627
    • Cooke, K.L.1    Grossman, Z.2
  • 10
    • 0004033107 scopus 로고    scopus 로고
    • Engelborghs K, Luzyanina T and Samaey G 2001 DDE-BIFTOOL v. 2.00: a Matlab package for bifurcation analysis of delay differential equations Technical Report TW-330 Department of Computer Science, K U Leuven, Leuven, Belgium
    • (2001) Technical Report
    • Engelborghs, K.1    Luzyanina, T.2    Samaey, G.3
  • 13
    • 0000028620 scopus 로고
    • Competition, decision, and consensus
    • Grossberg S 1978 Competition, decision, and consensus J. Math. Anal. Appl. 66 470-93
    • (1978) J. Math. Anal. Appl. , vol.66 , Issue.2 , pp. 470-493
    • Grossberg, S.1
  • 14
    • 0018860355 scopus 로고
    • Biological competition: Decision rules, pattern formation, and oscillations
    • Grossberg S 1980 Biological competition: decision rules, pattern formation, and oscillations Proc. Natl Acad. Sci. USA 77 2338-42
    • (1980) Proc. Natl Acad. Sci. USA , vol.77 , pp. 2338-2342
    • Grossberg, S.1
  • 16
    • 0041511877 scopus 로고    scopus 로고
    • Hopf bifurcating periodic orbits in a ring of neurons with delays
    • Guo S and Huang L 2003 Hopf bifurcating periodic orbits in a ring of neurons with delays Physica D 183 19-44
    • (2003) Physica , vol.183 , Issue.1-2 , pp. 19-44
    • Guo, S.1    Huang, L.2
  • 18
    • 0004469897 scopus 로고
    • Neurons with graded response have collective computational properties like those of two-state neurons
    • Hopfield J J 1984 Neurons with graded response have collective computational properties like those of two-state neurons Proc. Natl Acad. Sci. USA 81 3088-92
    • (1984) Proc. Natl Acad. Sci. USA , vol.81 , pp. 3088-3092
    • Hopfield, J.J.1
  • 19
    • 0020118274 scopus 로고
    • Neural networks and physical systems with emergent collective computational abilities
    • Hopfield J J 1982 Neural networks and physical systems with emergent collective computational abilities Proc. Natl Acad. Sci. USA 79 2554-8
    • (1982) Proc. Natl Acad. Sci. USA , vol.79 , pp. 2554-2558
    • Hopfield, J.J.1
  • 20
    • 0002175879 scopus 로고    scopus 로고
    • Computation formulae of an equivariant degree with applications to symmetric bifurcations
    • Krawcewicz W, Vivi P and Wu J 1997 Computation formulae of an equivariant degree with applications to symmetric bifurcations Nonlinear Studies 4 89-119
    • (1997) Nonlinear Studies , vol.4 , pp. 89-119
    • Krawcewicz, W.1    Vivi, P.2    Wu, J.3
  • 21
    • 0033102023 scopus 로고    scopus 로고
    • Theory and applications of Hopf bifurcations in symmetric functional-differential equations
    • Krawcewicz W and Wu J 1999 Theory and applications of Hopf bifurcations in symmetric functional-differential equations Nonlinear Anal. 35 845-70
    • (1999) Nonlinear Anal. , vol.35 , Issue.7 , pp. 845-870
    • Krawcewicz, W.1    Wu, J.2
  • 22
    • 0000380827 scopus 로고
    • Nonlinear dynamics and stability of analog neural networks
    • Marcus C M, Waugh F R and Westervelt R M 1991 Nonlinear dynamics and stability of analog neural networks Physica D 51 234-47
    • (1991) Physica , vol.51 , Issue.1-3 , pp. 234-247
    • Marcus, C.M.1    Waugh, F.R.2    Westervelt, R.M.3
  • 24
    • 0000256610 scopus 로고
    • Stability of analog neural networks with delay
    • Marcus C M and Westervelt R M 1989 Stability of analog neural networks with delay Phys. Rev. A 39 347-59
    • (1989) Phys. Rev. , vol.39 , Issue.1 , pp. 347-359
    • Marcus, C.M.1    Westervelt, R.M.2
  • 25
    • 12244313650 scopus 로고    scopus 로고
    • Change in criticality of synchronous Hopf bifurcation in a multiple-delayed neural system
    • Ncube I, Campbell S A and Wu J 2003 Change in criticality of synchronous Hopf bifurcation in a multiple-delayed neural system Dynamical Systems and their Applications to Biology (Fields Institute Communications vol 36) ed S Ruan et al (Providence, RI: American Mathematical Society) pp 179-93
    • (2003) Dynamical Systems and Their Applications to Biology , pp. 179-193
    • Ncube, I.1    Campbell, S.A.2    Wu, J.3
  • 26
    • 84867929802 scopus 로고    scopus 로고
    • Hopf bifurcation calculations in delayed systems with translational symmetry
    • Orosz G and Stépán G 2004 Hopf bifurcation calculations in delayed systems with translational symmetry J. Nonlinear Sci. 14 505-28
    • (2004) J. Nonlinear Sci. , vol.14 , Issue.6 , pp. 505-528
    • Orosz, G.1    Stépán, G.2
  • 27
    • 42749102192 scopus 로고    scopus 로고
    • Global bifurcation investigation of an optimal velocity traffic model with driver reaction time
    • Orosz G, Wilson R E and Krauskopf B 2004 Global bifurcation investigation of an optimal velocity traffic model with driver reaction time Phys. Rev. E 70 026207
    • (2004) Phys. Rev. , vol.70 , pp. 026207
    • Orosz, G.1    Wilson, R.E.2    Krauskopf, B.3
  • 28
    • 0342936163 scopus 로고    scopus 로고
    • Stability, bifurcation and multistability in a system of two coupled neurons with multiple time delays
    • Shayer L P and Campbell S A 2000 Stability, bifurcation and multistability in a system of two coupled neurons with multiple time delays SIAM J. Appl. Math. 61 673-700
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.2 , pp. 673-700
    • Shayer, L.P.1    Campbell, S.A.2
  • 29
    • 33646864830 scopus 로고    scopus 로고
    • Symmetric functional-differential equations and neural networks with memory
    • Wu J 1998 Symmetric functional-differential equations and neural networks with memory Trans. Am. Math. Soc. 350 4799-838
    • (1998) Trans. Am. Math. Soc. , vol.350 , Issue.12 , pp. 4799-4838
    • Wu, J.1
  • 30
    • 0033166162 scopus 로고    scopus 로고
    • Synchronization and stable phase-locking in a network of neurons with memory
    • Wu J, Faria T and Huang Y S 1999 Synchronization and stable phase-locking in a network of neurons with memory Math. Comput. Modelling 30 117-38
    • (1999) Math. Comput. Modelling , vol.30 , Issue.1-2 , pp. 117-138
    • Wu, J.1    Faria, T.2    Huang, Y.S.3
  • 31
    • 26944442186 scopus 로고    scopus 로고
    • Stability and synchronization of a ring of identical cells with delayed coupling
    • Yuan Y and Campbell S A 2004 Stability and synchronization of a ring of identical cells with delayed coupling J. Dyn. Diff. Eqns 16 709-44
    • (2004) J. Dyn. Diff. Eqns , vol.16 , Issue.3 , pp. 709-744
    • Yuan, Y.1    Campbell, S.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.