메뉴 건너뛰기




Volumn 14, Issue 8, 2004, Pages 2799-2810

Linear stability and Hopf bifurcation in a two-neuron network with three delays

Author keywords

Delay; Hopf bifurcation; Neural network; Stability

Indexed keywords

COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; FEEDBACK CONTROL; FUNCTIONS; MATHEMATICAL MODELS; NEURAL NETWORKS; NONLINEAR SYSTEMS; STABILITY; THEOREM PROVING;

EID: 4944247888     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127404011016     Document Type: Article
Times cited : (58)

References (20)
  • 1
    • 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. [1996] "Frustration, stability and delay-induced oscillations in a neural network model," SIAM J. Appl. Math. 48, 245-255.
    • (1996) SIAM J. Appl. Math. , vol.48 , pp. 245-255
    • Bélair, J.1    Campbell, S.A.2    Van Den Driessche, P.3
  • 2
    • 0002848816 scopus 로고    scopus 로고
    • Stability and bifurcation of a simple neural networks with multiple delays
    • Campbell, S. A. [1999] "Stability and bifurcation of a simple neural networks with multiple delays," Fields Inst. Commun. 21, 65-79.
    • (1999) Fields Inst. Commun. , vol.21 , pp. 65-79
    • Campbell, S.A.1
  • 3
    • 0020970741 scopus 로고
    • Absolute stability of global pattern formation and parallel memory storage by competitive neural networks
    • Cohen, M. A. & Grossberg, S. [1983] "Absolute stability of global pattern formation and parallel memory storage by competitive neural networks," IEEE Trans. Syst. Man Cybern. 13, 815-826.
    • (1983) IEEE Trans. Syst. Man Cybern. , vol.13 , pp. 815-826
    • Cohen, M.A.1    Grossberg, S.2
  • 5
    • 4944264860 scopus 로고    scopus 로고
    • Ermentrout, G. B. [1997] Department of Mathematics, University of Pittsburgh, Pittsburgh
    • Ermentrout, G. B. [1997] Department of Mathematics, University of Pittsburgh, Pittsburgh.
  • 6
    • 22244473030 scopus 로고    scopus 로고
    • Delay induced periodicity in a neural network of excitation and inhibition
    • Gopalsamy, K. & Leung, I. [1996] "Delay induced periodicity in a neural network of excitation and inhibition," Physica D89, 395-426.
    • (1996) Physica , vol.D89 , pp. 395-426
    • Gopalsamy, K.1    Leung, I.2
  • 9
    • 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. Nat. Acad. Sci. USA 81, 3088-3092.
    • (1984) Proc. Nat. Acad. Sci. USA , vol.81 , pp. 3088-3092
    • Hopfield, J.J.1
  • 10
    • 0000256610 scopus 로고
    • Stability of analog neural networks with delay
    • Marcus, C. M. & Westervelt, R. M. [1989] "Stability of analog neural networks with delay," Phys. Rev. A39, 347-359.
    • (1989) Phys. Rev. , vol.A39 , pp. 347-359
    • Marcus, C.M.1    Westervelt, R.M.2
  • 11
    • 0000380827 scopus 로고
    • Nonlinear dynamics and stability of analog neural networks
    • Marcus, C. M., Waugh, F. R. & Westervelt, R. M. [1991] "Nonlinear dynamics and stability of analog neural networks," Physica D51, 234-247.
    • (1991) Physica , vol.D51 , pp. 234-247
    • Marcus, C.M.1    Waugh, F.R.2    Westervelt, R.M.3
  • 12
    • 0001082564 scopus 로고    scopus 로고
    • Bifurcations, stability and monotonicity propertities of a delayed neural network model
    • Olien, L. & Bélair, J. [1997] "Bifurcations, stability and monotonicity propertities of a delayed neural network model," Physica D102, 349-363.
    • (1997) Physica , vol.D102 , pp. 349-363
    • Olien, L.1    Bélair, J.2
  • 13
    • 0001266424 scopus 로고    scopus 로고
    • Transient regime duration in continuous-time neural networks with delay
    • Pakdaman, K., Grotte-Ragazzo, C. & Malta, C. P. [1998a] "Transient regime duration in continuous-time neural networks with delay," Phys. Rev. E58, 3623-3627.
    • (1998) Phys. Rev. , vol.E58 , pp. 3623-3627
    • Pakdaman, K.1    Grotte-Ragazzo, C.2    Malta, C.P.3
  • 14
    • 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. [1998b] "Effect of delay on the boundary of the basin of attraction in a system of two neurons," Neural Networks 11, 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
  • 15
    • 33746961598 scopus 로고    scopus 로고
    • Periodic solutions of planar systems with two delays
    • Ruan, S. & Wei, J. [1999] "Periodic solutions of planar systems with two delays," Proc. Roy. Soc. Edinburgh A129, 1017-1032.
    • (1999) Proc. Roy. Soc. Edinburgh , vol.A129 , pp. 1017-1032
    • Ruan, S.1    Wei, J.2
  • 16
    • 0342936163 scopus 로고    scopus 로고
    • Stability, bifurcation, and multistability in a system of two coupled neurons with multiple time delays
    • Shayer, L. & 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 , pp. 673-700
    • Shayer, L.1    Campbell, S.A.2
  • 17
    • 0023317858 scopus 로고
    • Neural computation by concentrating information in time
    • Tank, D. W. & Hopfield, J. J. [1987] "Neural computation by concentrating information in time," Proc. Nat. Acad. Sci. USA 84, 1896-1900.
    • (1987) Proc. Nat. Acad. Sci. USA , vol.84 , pp. 1896-1900
    • Tank, D.W.1    Hopfield, J.J.2
  • 18
    • 0347130009 scopus 로고    scopus 로고
    • Stability and bifurcation in a neural network model with two delays
    • Wei, J. & Ruan, S. [1999] "Stability and bifurcation in a neural network model with two delays," Physica D130, 255-272.
    • (1999) Physica , vol.D130 , pp. 255-272
    • Wei, J.1    Ruan, S.2
  • 19
    • 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. Amer. Math. Soc. 350, 4799-4838.
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 4799-4838
    • Wu, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.