메뉴 건너뛰기




Volumn 183, Issue 1-2, 2003, Pages 19-44

Hopf bifurcating periodic orbits in a ring of neurons with delays

Author keywords

A ring of neurons; Hopf bifurcation; Lie group; Slowly oscillating periodic solution

Indexed keywords

BIFURCATION (MATHEMATICS); DIFFERENTIAL EQUATIONS; FEEDBACK; ORBITS; OSCILLATIONS;

EID: 0041511877     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(03)00159-3     Document Type: Article
Times cited : (157)

References (33)
  • 1
    • 0042794508 scopus 로고
    • Bifurcation of zeros of parameterized functions
    • Alexander J.C., Bifurcation of zeros of parameterized functions. J. Funct. Anal. 29:1978;37-53.
    • (1978) J. Funct. Anal. , vol.29 , pp. 37-53
    • Alexander, J.C.1
  • 2
  • 3
    • 0018615307 scopus 로고
    • Delays in physiological systems
    • an der Heiden U., Delays in physiological systems. J. Math. Biol. 8:1978;345-364.
    • (1978) J. Math. Biol. , vol.8 , pp. 345-364
    • An der Heiden, U.1
  • 4
    • 0038346765 scopus 로고
    • Participation of inhibitory interneurons in the control of hippocampal cortical output
    • M. Brazier (Ed.), University of California Press, Los Angeles, CA
    • P. Anderson, O. Gross, T. Lomo, et al., Participation of inhibitory interneurons in the control of hippocampal cortical output, in: M. Brazier (Ed.), The Interneuron, University of California Press, Los Angeles, CA, 1969.
    • (1969) The Interneuron
    • Anderson, P.1    Gross, O.2    Lomo, T.3
  • 5
    • 0030081051 scopus 로고    scopus 로고
    • Frustration, stability and delay-induced oscillations in a neural network model
    • Bélair J., Campbell S.A., van den Driessche P., Frustration, stability and delay-induced oscillations in a neural network model. SIAM J. Appl. Math. 46:1996;245-255.
    • (1996) SIAM J. Appl. Math. , vol.46 , pp. 245-255
    • Bélair, J.1    Campbell, S.A.2    Van den Driessche, P.3
  • 6
    • 0002848816 scopus 로고    scopus 로고
    • Stability and bifurcation of a simple neural network with multiple time delays
    • S. Ruan, G.S.K. Wolkowicz, J. Wu (Eds.), Fields Institute Communications, AMS, Providence, RI
    • S.A. Campbell, Stability and bifurcation of a simple neural network with multiple time delays, in: S. Ruan, G.S.K. Wolkowicz, J. Wu (Eds.), Differential Equations with Application to Biology, vol. 21, Fields Institute Communications, AMS, Providence, RI, 1998, pp. 65-79.
    • (1998) Differential Equations with Application to Biology , vol.21 , pp. 65-79
    • Campbell, S.A.1
  • 7
    • 23044521116 scopus 로고    scopus 로고
    • Desynchronization of large scale delayed neural networks
    • Chen Y., Huang Y., Wu J., Desynchronization of large scale delayed neural networks. Proc. Am. Math. Soc. 128(8):2000;2365-2371.
    • (2000) Proc. Am. Math. Soc. , vol.128 , Issue.8 , pp. 2365-2371
    • Chen, Y.1    Huang, Y.2    Wu, J.3
  • 8
    • 0020970741 scopus 로고
    • Absolute stability of global pattern formation and parallel memory storage by competitive neural networks
    • Cohen M.A., Grossberg S., Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybernet. 13:1983;815-826.
    • (1983) IEEE Trans. Syst. Man Cybernet. , vol.13 , pp. 815-826
    • Cohen, M.A.1    Grossberg, S.2
  • 9
    • 0003196710 scopus 로고
    • Integrodifferential equations and delay models in population dynamics
    • Springer, New York
    • J.M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics, vol. 20, Springer, New York, 1977.
    • (1977) Lecture Notes in Biomathematics , vol.20
    • Cushing, J.M.1
  • 11
    • 0040335747 scopus 로고
    • 1 -degree and global Hopf bifurcation theory of functional differential equations
    • 1 -degree and global Hopf bifurcation theory of functional differential equations J. Diff. Eq. 98:1992;227-298.
    • (1992) J. Diff. Eq. , vol.98 , pp. 227-298
    • Erbe, L.H.1    Krawcewicz, W.2    Geba, K.3    Wu, J.4
  • 13
    • 0000840164 scopus 로고
    • Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
    • Faria T., Magalháes L.T., Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation. J. Diff. Eq. 122:1995;181-200.
    • (1995) J. Diff. Eq. , vol.122 , pp. 181-200
    • Faria, T.1    Magalháes, L.T.2
  • 14
    • 0003250925 scopus 로고
    • Global bifurcation of periodic solutions with symmetry
    • Springer, New York
    • B. Fiedler, Global Bifurcation of Periodic Solutions with Symmetry, Lecture Notes in Mathematics, vol. 1309, Springer, New York, 1988.
    • (1988) Lecture Notes in Mathematics , vol.1309
    • Fiedler, B.1
  • 16
    • 22244473030 scopus 로고    scopus 로고
    • Delay induced periodicity in a neural network of excitation and inhibition
    • Gopalsamy K., Leung I., Delay induced periodicity in a neural network of excitation and inhibition. Physica D. 89:1996;395-426.
    • (1996) Physica D , vol.89 , pp. 395-426
    • Gopalsamy, K.1    Leung, I.2
  • 19
    • 0024909476 scopus 로고
    • Convergent activation dynamics in continuous-time networks
    • Hirsch M.W., Convergent activation dynamics in continuous-time networks. Neural Networks. 2:1989;331-349.
    • (1989) Neural Networks , vol.2 , pp. 331-349
    • Hirsch, M.W.1
  • 20
    • 0004469897 scopus 로고
    • Neurons with graded response have collective computational properties like those of two-state neurons
    • Hopfield J.J., Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA. 81:1984;3088-3092.
    • (1984) Proc. Natl. Acad. Sci. USA , vol.81 , pp. 3088-3092
    • Hopfield, J.J.1
  • 21
    • 0038381865 scopus 로고    scopus 로고
    • Nonlinear waves in networks of neurons with delayed feedback: Pattern formation and continuation
    • Huang L., Wu J., Nonlinear waves in networks of neurons with delayed feedback: pattern formation and continuation. SIAM J. Math. Anal. 34(4):2003;836-860.
    • (2003) SIAM J. Math. Anal. , vol.34 , Issue.4 , pp. 836-860
    • Huang, L.1    Wu, J.2
  • 22
    • 0001149792 scopus 로고
    • A folk theorem in functional differential equations
    • Levinger B.W., A folk theorem in functional differential equations. J. Diff. Eq. 4:1968;612-619.
    • (1968) J. Diff. Eq. , vol.4 , pp. 612-619
    • Levinger, B.W.1
  • 23
    • 0000256610 scopus 로고
    • Stability of analog neural networks with delay
    • Marcus C.M., Westervelt R.M., Stability of analog neural networks with delay. Phys. Rev. A. 39:1989;347-359.
    • (1989) Phys. Rev. A , vol.39 , pp. 347-359
    • Marcus, C.M.1    Westervelt, R.M.2
  • 24
    • 0001082564 scopus 로고    scopus 로고
    • Bifurcations, stability and monotonicity properties of a delayed neural network model
    • Olien L., Bélair J., Bifurcations, stability and monotonicity properties of a delayed neural network model. Physica D. 102:1997;349-363.
    • (1997) Physica D , vol.102 , pp. 349-363
    • Olien, L.1    Bélair, J.2
  • 25
    • 0015128941 scopus 로고
    • Instability and dynamics pattern in cellular networks
    • Othmer H.G., Scriven L.E., Instability and dynamics pattern in cellular networks. J. Theor. Biol. 32:1971;507-537.
    • (1971) J. Theor. Biol. , vol.32 , pp. 507-537
    • Othmer, H.G.1    Scriven, L.E.2
  • 26
    • 0001266424 scopus 로고    scopus 로고
    • Transient regime duration in continuous-time neural networks with delay
    • Pakdaman K., Grotta-Ragazzo C., Malta C.P., Transient regime duration in continuous-time neural networks with delay. Phys. Rev. E. 58:1998;3623-3627.
    • (1998) Phys. Rev. E , vol.58 , pp. 3623-3627
    • Pakdaman, K.1    Grotta-Ragazzo, C.2    Malta, C.P.3
  • 27
    • 0032052445 scopus 로고    scopus 로고
    • Effect of delay on the boundary of the basin of attraction in a system of two neurons
    • Pakdaman K., Grotta-Ragazzo C., Malta C.P., Arino O., Vibert J.-F., Effect of delay on the boundary of the basin of attraction in a system of two neurons. Neural Networks. 11:1998;509-519.
    • (1998) Neural Networks , vol.11 , pp. 509-519
    • Pakdaman, K.1    Grotta-Ragazzo, C.2    Malta, C.P.3    Arino, O.4    Vibert, J.-F.5
  • 28
    • 84966222614 scopus 로고
    • Bifurcation and symmetry breaking in applied mathematics
    • Sattinger D.H., Bifurcation and symmetry breaking in applied mathematics. Bull. Am. Math. Soc. 3:1980;779-819.
    • (1980) Bull. Am. Math. Soc. , vol.3 , pp. 779-819
    • Sattinger, D.H.1
  • 29
    • 0016797259 scopus 로고
    • The module-concept in cerebral cortex architecture
    • Szenfagothai J., The module-concept in cerebral cortex architecture. Brain Res. 95:1967;475-496.
    • (1967) Brain Res. , vol.95 , pp. 475-496
    • Szenfagothai, J.1
  • 30
    • 0023317858 scopus 로고
    • Neural computation by concentrating information in time
    • Tank D.W., Hopfield J.J., Neural computation by concentrating information in time. Proc. Natl. Acad. Sci. USA. 84:1987;1896-1900.
    • (1987) Proc. Natl. Acad. Sci. USA , vol.84 , pp. 1896-1900
    • Tank, D.W.1    Hopfield, J.J.2
  • 31
    • 0040663274 scopus 로고
    • Hopf bifurcation and symmetry: Standing and traveling waves in a circular-chain
    • van Gils S.A., Valkering T., Hopf bifurcation and symmetry: standing and traveling waves in a circular-chain. Jpn. J. Appl. Math. 3:1986;207-222.
    • (1986) Jpn. J. Appl. Math. , vol.3 , pp. 207-222
    • Van Gils, S.A.1    Valkering, T.2
  • 32
    • 33646864830 scopus 로고    scopus 로고
    • Symmetric functional differential equations and neural networks with memory
    • Wu J., Symmetric functional differential equations and neural networks with memory. Trans. Am. Math. Soc. 350(12):1998;4799-4838.
    • (1998) Trans. Am. Math. Soc. , vol.350 , Issue.12 , pp. 4799-4838
    • Wu, J.1
  • 33
    • 0033166162 scopus 로고    scopus 로고
    • Synchronization and stable phase-locking in a network of neurons with memory
    • Wu J., Synchronization and stable phase-locking in a network of neurons with memory. Math. Comp. Model. 30(1-2):1999;117-138.
    • (1999) Math. Comp. Model. , vol.30 , Issue.1-2 , pp. 117-138
    • Wu, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.