메뉴 건너뛰기




Volumn 259, Issue 1, 2001, Pages 188-208

Slowly oscillating periodic solutions for a delayed frustrated network of two neurons

Author keywords

Cyclic system; Delayed frustrated network; Discrete Lyapunov functional; Eigenvalue; Slowly oscillating periodic orbit

Indexed keywords


EID: 0035402689     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7410     Document Type: Article
Times cited : (48)

References (19)
  • 1
    • 0018505051 scopus 로고
    • Periodic solutions of a nonlinear second order differential equation with delay
    • an der Heiden U. Periodic solutions of a nonlinear second order differential equation with delay. J. Math. Anal. Appl. 70:1979;599-609.
    • (1979) J. Math. Anal. Appl. , vol.70 , pp. 599-609
    • An Der Heiden, U.1
  • 2
    • 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
  • 3
    • 0030594503 scopus 로고    scopus 로고
    • On the existence and global bifurcation of periodic solutions to planar differential delay equations
    • Baptistini M. Z., Táboas P. Z. On the existence and global bifurcation of periodic solutions to planar differential delay equations. J. Differential Equations. 127:1996;391-425.
    • (1996) J. Differential Equations , vol.127 , pp. 391-425
    • Baptistini, M.Z.1    Táboas, P.Z.2
  • 5
    • 0038346772 scopus 로고    scopus 로고
    • Existence and attraction of a phase-locked oscillation in a delayed network of two neurons
    • Chen Y., Wu J. Existence and attraction of a phase-locked oscillation in a delayed network of two neurons. Integral and Differential Equations. 2001.
    • (2001) Integral and Differential Equations
    • Chen, Y.1    Wu, J.2
  • 8
    • 22244473030 scopus 로고    scopus 로고
    • Delay induced periodicity in a neural netlet of excitation and inhibition
    • Gopalsamy K., Leung I. Delay induced periodicity in a neural netlet of excitation and inhibition. Physica D. 89:1996;395-426.
    • (1996) Physica D , vol.89 , pp. 395-426
    • Gopalsamy, K.1    Leung, I.2
  • 9
    • 0020118274 scopus 로고
    • Neural networks and physical systems with emergent collective computational abilities
    • Hopfield J. J. Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. 79:1982;2554-2558.
    • (1982) Proc. Nat. Acad. Sci. , vol.79 , pp. 2554-2558
    • Hopfield, J.J.1
  • 10
    • 0004469897 scopus 로고
    • Neurons with graded response have collective computational properties like two-stage neurons
    • Hopfield J. J. Neurons with graded response have collective computational properties like two-stage neurons. Proc. Nat. Acad. Sci. 81:1984;3088-3092.
    • (1984) Proc. Nat. Acad. Sci. , vol.81 , pp. 3088-3092
    • Hopfield, J.J.1
  • 11
    • 0003265680 scopus 로고    scopus 로고
    • Shape, Smoothness and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback
    • Providence: Am. Math. Soc.
    • Krisztin T., Walther H.-O., Wu J. Shape, Smoothness and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback. Fields Institute Monographs. 11:1999;Am. Math. Soc. Providence.
    • (1999) Fields Institute Monographs , vol.11
    • Krisztin, T.1    Walther, H.-O.2    Wu, J.3
  • 12
    • 0030102662 scopus 로고    scopus 로고
    • Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions
    • Mallet-Paret J., Sell G. R. Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions. J. Differential Equations. 125:1996;385-440.
    • (1996) J. Differential Equations , vol.125 , pp. 385-440
    • Mallet-Paret, J.1    Sell, G.R.2
  • 13
    • 0030102885 scopus 로고    scopus 로고
    • The Poincaré-Bendixson theorem for monotone cyclic feedback system with delay
    • Mallet-Paret J., Sell G. R. The Poincaré-Bendixson theorem for monotone cyclic feedback system with delay. J. Differential Equations. 125:1996;441-489.
    • (1996) J. Differential Equations , vol.125 , pp. 441-489
    • Mallet-Paret, J.1    Sell, G.R.2
  • 14
    • 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;347-356.
    • (1989) Phys. Rev. A , vol.39 , pp. 347-356
    • Marcus, C.M.1    Westervelt, R.M.2
  • 15
    • 0002971208 scopus 로고
    • On the zeros of some elementary transcendental functions
    • Pontryagin L. On the zeros of some elementary transcendental functions. Amer. Math. Soc. Transl. Ser. 2. 1:1955;95-110.
    • (1955) Amer. Math. Soc. Transl. Ser. 2 , vol.1 , pp. 95-110
    • Pontryagin, L.1
  • 16
    • 33746961598 scopus 로고    scopus 로고
    • Periodic solutions of planar systems with two delays
    • Ruan S., Wei J. Periodic solutions of planar systems with two delays. Proc. Roy. Soc. Edinburgh Sect. A. 129:1999;1017-1032.
    • (1999) Proc. Roy. Soc. Edinburgh Sect. A , vol.129 , pp. 1017-1032
    • Ruan, S.1    Wei, J.2
  • 17
    • 0001243427 scopus 로고
    • Monotone semiflows generated by functional differential equations
    • Smith H. L. Monotone semiflows generated by functional differential equations. J. Differential Equations. 66:1987;420-442.
    • (1987) J. Differential Equations , vol.66 , pp. 420-442
    • Smith, H.L.1
  • 18
    • 0002885593 scopus 로고
    • Periodic solutions of a planar delay equation
    • Táboas P. Periodic solutions of a planar delay equation. Proc. Roy. Soc. Edinburgh Sect. A. 116:1990;85-101.
    • (1990) Proc. Roy. Soc. Edinburgh Sect. A , vol.116 , pp. 85-101
    • Táboas, P.1
  • 19
    • 0002684591 scopus 로고
    • An invariant manifold of slowly oscillating solutions for x′(t) = -μx(t) + f(x(t - 1))
    • Walther H.-O. An invariant manifold of slowly oscillating solutions for x′(t) = -μx(t) + f(x(t - 1)). J. Reine Angew. Math. 414:1991;67-112.
    • (1991) J. Reine Angew. Math. , vol.414 , pp. 67-112
    • Walther, H.-O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.