메뉴 건너뛰기




Volumn 18, Issue 10, 2008, Pages 3053-3072

Stability and hopf bifurcation of a delayed network of four neurons with a short-cut connection

Author keywords

Hopf bifurcation; Neural networks; Short cut connection; Time delay

Indexed keywords

BIFURCATION (MATHEMATICS); CIRCUIT SIMULATION; NEURAL NETWORKS; NUMERICAL MODELS; TIME DELAY;

EID: 59049104858     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021812740802224X     Document Type: Article
Times cited : (15)

References (31)
  • 1
    • 42749102623 scopus 로고    scopus 로고
    • Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling
    • Burić, N. & Todorović, D. [2003] "Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling," Phys. Rev. E 67, 066222.
    • (2003) Phys. Rev. E , vol.67 , pp. 066222
    • Burić, N.1    Todorović, D.2
  • 3
    • 32844462800 scopus 로고    scopus 로고
    • Multistability and stable asynchronous periodic oscillations in a multiple-delayed neural system
    • Campbell, S. A., Ncube, I. & Wu, J. [2006] "Multistability and stable asynchronous periodic oscillations in a multiple-delayed neural system," Physica D 214, 101-119.
    • (2006) Physica D , vol.214 , pp. 101-119
    • Campbell, S.A.1    Ncube, I.2    Wu, J.3
  • 5
    • 22244473030 scopus 로고    scopus 로고
    • Delay induced periodicity in a neural netlet of excitation and inhibition
    • Gopalsamy, K. & Leung, I. [1996] "Delay induced periodicity in a neural netlet of excitation and inhibition," Physica D 89, 395-426.
    • (1996) Physica D , vol.89 , pp. 395-426
    • Gopalsamy, K.1    Leung, I.2
  • 6
    • 0041511877 scopus 로고    scopus 로고
    • Hopf bifurcating periodic orbits in a ring of neurons with delays
    • Guo, S. J. & Huang, L. H. [2003] "Hopf bifurcating periodic orbits in a ring of neurons with delays," Physica D 183, 19-44.
    • (2003) Physica D , vol.183 , pp. 19-44
    • Guo, S.J.1    Huang, L.H.2
  • 7
    • 34547092964 scopus 로고    scopus 로고
    • Stability bifurcation and global existence of a Hopf-bifurcating periodic solution for a class of three-neuron delayed network models
    • Gupta, P. D., Majee, N. C. & Roy, A. B. [2007] "Stability bifurcation and global existence of a Hopf-bifurcating periodic solution for a class of three-neuron delayed network models," Nonlin. Anal. Th. Meth. Appl. 67, 2934-2954.
    • (2007) Nonlin. Anal. Th. Meth. Appl , vol.67 , pp. 2934-2954
    • Gupta, P.D.1    Majee, N.C.2    Roy, A.B.3
  • 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
  • 11
    • 34247122734 scopus 로고    scopus 로고
    • Hopf bifurcation analysis for a twoneuron network with four delays
    • Huang, C. X., Huang, L. H., Feng, J. F., Nai, M. Y. & He, Y. G. [2007] "Hopf bifurcation analysis for a twoneuron network with four delays," Chaos Solit. Fract. 34, 795-812.
    • (2007) Chaos Solit. Fract , vol.34 , pp. 795-812
    • Huang, C.X.1    Huang, L.H.2    Feng, J.F.3    Nai, M.Y.4    He, Y.G.5
  • 12
    • 0035832866 scopus 로고    scopus 로고
    • Chaos in a three-neuron hysteresis Hopfied-type neural network
    • Li, C. G., Yu, J. B. & Liao, X. F. [2001] "Chaos in a three-neuron hysteresis Hopfied-type neural network," Phys. Lett. A 285, 368-372.
    • (2001) Phys. Lett. A , vol.285 , pp. 368-372
    • Li, C.G.1    Yu, J.B.2    Liao, X.F.3
  • 13
    • 34248519240 scopus 로고    scopus 로고
    • Stability and bifurcation analysis in tri-neuron model with time delay
    • Liao, X. F., Guo, S. T. & Li, C. D. [2007] "Stability and bifurcation analysis in tri-neuron model with time delay," Nontin. Dyn. 49, 319-345.
    • (2007) Nontin. Dyn , vol.49 , pp. 319-345
    • Liao, X.F.1    Guo, S.T.2    Li, C.D.3
  • 14
    • 0000256610 scopus 로고
    • Stability of analog neural network with delay
    • Marcus, C. M. & Westervelt, R. M. [1989] "Stability of analog neural network with delay," Phys. Rev. A 39, 347-359.
    • (1989) Phys. Rev. A , vol.39 , pp. 347-359
    • Marcus, C.M.1    Westervelt, R.M.2
  • 16
    • 38349094163 scopus 로고    scopus 로고
    • Order reduction of retarded nonlinear systems - the method of multiple scales versus center-manifold reduction
    • Nayfeh, A. H. [2008] "Order reduction of retarded nonlinear systems - the method of multiple scales versus center-manifold reduction," Nonlin. Dyn. 51, 483-500.
    • (2008) Nonlin. Dyn , vol.51 , pp. 483-500
    • Nayfeh, A.H.1
  • 17
    • 0033487710 scopus 로고    scopus 로고
    • Scaling and percolation in the small-world network model
    • Newman, M. E. J. & Watts, D. J. [1999] "Scaling and percolation in the small-world network model," Phys. Rev. E 60, 7332-7342.
    • (1999) Phys. Rev. E , vol.60 , pp. 7332-7342
    • Newman, M.E.J.1    Watts, D.J.2
  • 18
    • 0038718854 scopus 로고    scopus 로고
    • The structure and function of complex networks
    • Newman, M. E. J. [2003] "The structure and function of complex networks," SLAM Rev. 45, 167-256.
    • (2003) SLAM Rev , vol.45 , pp. 167-256
    • Newman, M.E.J.1
  • 19
    • 0001082564 scopus 로고    scopus 로고
    • Bifurcations, stability, and monotonicity properties of a delayed neural network model
    • Olien, L. & Bélair, J. [1997] "Bifurcations, stability, and monotonicity properties of a delayed neural network model," Physica D 102, 349-363.
    • (1997) Physica D , vol.102 , pp. 349-363
    • Olien, L.1    Bélair, J.2
  • 20
    • 0342936163 scopus 로고    scopus 로고
    • Stability bifurcation and multistability in a system of two coupled neurons with multiple time delays
    • Shayer, L. P. & 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.P.1    Campbell, S.A.2
  • 21
    • 19844368134 scopus 로고    scopus 로고
    • Time-delay enhanced synchronization and regularization in two coupled chaotic neurons
    • Wang, Q. Y. & Lu, Q. S. [2005] "Time-delay enhanced synchronization and regularization in two coupled chaotic neurons," Chinese Phys. Lett. 22, 543-546.
    • (2005) Chinese Phys. Lett , vol.22 , pp. 543-546
    • Wang, Q.Y.1    Lu, Q.S.2
  • 22
    • 0033682963 scopus 로고    scopus 로고
    • Stability switches of dynamic systems with unknown parameters
    • Wang, Z. H. & Hu, H. Y. [2000] "Stability switches of dynamic systems with unknown parameters," J. Sound Vibr. 233, 215-233.
    • (2000) J. Sound Vibr , vol.233 , pp. 215-233
    • Wang, Z.H.1    Hu, H.Y.2
  • 23
    • 0032482432 scopus 로고    scopus 로고
    • Collective dynamics of 'small-world' networks
    • Watts, D. J. & Strogatz, S. H. [1998] "Collective dynamics of 'small-world' networks," Nature 393, 440-442.
    • (1998) Nature , vol.393 , pp. 440-442
    • Watts, D.J.1    Strogatz, S.H.2
  • 24
    • 0347130009 scopus 로고    scopus 로고
    • Stability and bifurcation in a neural network model with two delays
    • Wei, J. J. & Ruan, S. [1999] "Stability and bifurcation in a neural network model with two delays," Physica D 130, 255-272.
    • (1999) Physica D , vol.130 , pp. 255-272
    • Wei, J.J.1    Ruan, S.2
  • 25
    • 33847682304 scopus 로고    scopus 로고
    • Dynamics of a two dimensional delayed small-world network under delayed feedback control
    • Xu, X., Hu, H. Y. & Wang, H. L. [2006] "Dynamics of a two dimensional delayed small-world network under delayed feedback control," Int. J. Bifurcation and Chaos 16, 3257-3273.
    • (2006) Int. J. Bifurcation and Chaos , vol.16 , pp. 3257-3273
    • Xu, X.1    Hu, H.Y.2    Wang, H.L.3
  • 26
    • 33746239186 scopus 로고    scopus 로고
    • Hopf bifurcation and stability for a delayed tri-neuron network model
    • Yan, X. P. [2006] "Hopf bifurcation and stability for a delayed tri-neuron network model," J. Corn-put. Appl. Math. 196, 579-595.
    • (2006) J. Corn-put. Appl. Math , vol.196 , pp. 579-595
    • Yan, X.P.1
  • 27
    • 0035306020 scopus 로고    scopus 로고
    • Chaos in small-world networks
    • Yang, X. S. [2001] "Chaos in small-world networks," Phys. Rev. E 63, 046206.
    • (2001) Phys. Rev. E , vol.63 , pp. 046206
    • Yang, X.S.1
  • 28
    • 31744442908 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays
    • Yu, W. W. & Cao, J. D. [2006] "Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays," Phys. Lett. A 351, 64-78.
    • (2006) Phys. Lett. A , vol.351 , pp. 64-78
    • Yu, W.W.1    Cao, J.D.2
  • 29
    • 26944442186 scopus 로고    scopus 로고
    • Stability and synchronization of a ring of identical cells with delayed coupling
    • Yuan, Y. & Campbell, S. A. [2004] "Stability and synchronization of a ring of identical cells with delayed coupling," J. Dyn. Diff. Eq. 16, 709-744.
    • (2004) J. Dyn. Diff. Eq , vol.16 , pp. 709-744
    • Yuan, Y.1    Campbell, S.A.2
  • 30
    • 33847049750 scopus 로고    scopus 로고
    • Dynamics in a delayed neural network
    • Yuan, Y. [2007] "Dynamics in a delayed neural network," Chaos Solit. Fract. 33, 443-454.
    • (2007) Chaos Solit. Fract , vol.33 , pp. 443-454
    • Yuan, Y.1
  • 31
    • 0942299370 scopus 로고    scopus 로고
    • Chaos and its synchronization in two-neuron systems with discrete delays
    • Zhou, S. B., Liao, X. F., Yu, J. B. & Wong, K. W. [2004] "Chaos and its synchronization in two-neuron systems with discrete delays," Chaos Solit. Fract. 21, 133-142.
    • (2004) Chaos Solit. Fract , vol.21 , pp. 133-142
    • Zhou, S.B.1    Liao, X.F.2    Yu, J.B.3    Wong, K.W.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.