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Volumn 49, Issue 1-2, 2007, Pages 319-345

Stability and bifurcation analysis in tri-neuron model with time delay

Author keywords

Bifurcation; Global asymptotic stability; Local stability; Neural networks; Time delay

Indexed keywords

BIFURCATION (MATHEMATICS); LINEAR SYSTEMS; LYAPUNOV FUNCTIONS; MATHEMATICAL MODELS; NEURAL NETWORKS; NUMERICAL METHODS; TIME DELAY;

EID: 34248519240     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-006-9137-6     Document Type: Article
Times cited : (46)

References (43)
  • 1
    • 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. U.S.A. 81, 3088-3092 (1984)
    • (1984) Proc. Natl. Acad. Sci. U.S.A , vol.81 , pp. 3088-3092
    • Hopfield, J.J.1
  • 4
    • 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, 347-359 (1989)
    • (1989) Phys. Rev. A , vol.39 , pp. 347-359
    • Marcus, C.M.1    Westervelt, R.M.2
  • 5
    • 0028468031 scopus 로고
    • How delays affect neural dynamics and learning
    • Baldi, P., Atiya, A.F.: How delays affect neural dynamics and learning. IEEE Trans. Neural Networks, 612-621 (1994)
    • (1994) IEEE Trans. Neural Networks , vol.612-621
    • Baldi, P.1    Atiya, A.F.2
  • 6
    • 0001082564 scopus 로고    scopus 로고
    • Bifurcation, stability and monotonicity properties of a delayed neural model
    • Olien, L., Belair, J.: Bifurcation, stability and monotonicity properties of a delayed neural model. Physica D 102, 349-363 (1997)
    • (1997) Physica D , vol.102 , pp. 349-363
    • Olien, L.1    Belair, J.2
  • 7
    • 0012807025 scopus 로고    scopus 로고
    • Stability in a three-dimensional system of delay-differential equations
    • Belair, J., Dufour, S.: Stability in a three-dimensional system of delay-differential equations. Can. Appl. Math. Quart. 4, 1878-1890 (1998)
    • (1998) Can. Appl. Math. Quart , vol.4 , pp. 1878-1890
    • Belair, J.1    Dufour, S.2
  • 8
    • 0028542772 scopus 로고
    • Delay-independent stability in bidirectional associative memory networks
    • Gopalsamy, K., He, X.: Delay-independent stability in bidirectional associative memory networks. IEEE Trans. Neural Network 5, 998-1002 (1994)
    • (1994) IEEE Trans. Neural Network , vol.5 , pp. 998-1002
    • Gopalsamy, K.1    He, X.2
  • 9
    • 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, 395-426 (1996)
    • (1996) Physica D , vol.89 , pp. 395-426
    • Gopalsamy, K.1    Leung, I.2
  • 10
    • 0031101884 scopus 로고    scopus 로고
    • Convergence under dynamical thresholds with delays
    • Gopalsamy, K., Leung, I.: Convergence under dynamical thresholds with delays. IEEE Trans. Neural Network 8(2), 341-348 (1997)
    • (1997) IEEE Trans. Neural Network , vol.8 , Issue.2 , pp. 341-348
    • Gopalsamy, K.1    Leung, I.2
  • 11
    • 0001741180 scopus 로고    scopus 로고
    • Global Hopf-bifurcation in a neural netlet
    • Gopalsamy, K., Leung, I., Liu, P.: Global Hopf-bifurcation in a neural netlet. Appl. Math. Comput. 94, 171-192 (1998)
    • (1998) Appl. Math. Comput , vol.94 , pp. 171-192
    • Gopalsamy, K.1    Leung, I.2    Liu, P.3
  • 12
    • 0347130009 scopus 로고    scopus 로고
    • Stability and bifurcation in a neural network model with two delays
    • Wei, J., Ruan, S.: Stability and bifurcation in a neural network model with two delays. Physica D 130, 255-272 (1999)
    • (1999) Physica D , vol.130 , pp. 255-272
    • Wei, J.1    Ruan, S.2
  • 13
    • 0012869306 scopus 로고
    • Dynamics of simple electronic neural networks with added inertia
    • Babcock, K.L., Westervelt, R.M.: Dynamics of simple electronic neural networks with added inertia. Physica D 23, 464-469 (1986)
    • (1986) Physica D , vol.23 , pp. 464-469
    • Babcock, K.L.1    Westervelt, R.M.2
  • 14
    • 0023435167 scopus 로고
    • Dynamics of simple electronic neural networks
    • Babcock, K.L., Westervelt, R.M.: Dynamics of simple electronic neural networks. Physica D 28, 305-316 (1987)
    • (1987) Physica D , vol.28 , pp. 305-316
    • Babcock, K.L.1    Westervelt, R.M.2
  • 15
    • 0002785178 scopus 로고
    • Stability of periodic oscillation in a network of neurons with time delay
    • Destxhe, A.: Stability of periodic oscillation in a network of neurons with time delay. Phys. Lett. A 187, 309-316 (1994)
    • (1994) Phys. Lett. A , vol.187 , pp. 309-316
    • Destxhe, A.1
  • 16
    • 0002848816 scopus 로고    scopus 로고
    • Stability and bifurcation of a simple neural network with multiple time delays
    • Campbell, S.A.: Stability and bifurcation of a simple neural network with multiple time delays. Fields Inst. Commun. 21, 65-79 (1999)
    • (1999) Fields Inst. Commun , vol.21 , pp. 65-79
    • Campbell, S.A.1
  • 17
    • 0018615307 scopus 로고    scopus 로고
    • An der Heiden, U, Delays in physiological systems. J. Math. Biol. 8, 345-364 1979
    • An der Heiden, U.: Delays in physiological systems. J. Math. Biol. 8, 345-364 (1979)
  • 18
    • 0015260274 scopus 로고
    • Excitatory and inhibitory interactions in locallized populations of model neurons
    • Willson, H.R., Cowan, J.D.: Excitatory and inhibitory interactions in locallized populations of model neurons. Biophys. J. 12, 1-24 (1972)
    • (1972) Biophys. J , vol.12 , pp. 1-24
    • Willson, H.R.1    Cowan, J.D.2
  • 19
    • 0012889927 scopus 로고
    • Bursting oscillations from a homoclinic tangency in a time delat system
    • Destexhe, A., Gaspard, P.: Bursting oscillations from a homoclinic tangency in a time delat system. Phys. Lett. A 173, 386-391 (1993)
    • (1993) Phys. Lett. A , vol.173 , pp. 386-391
    • Destexhe, A.1    Gaspard, P.2
  • 20
    • 0031276105 scopus 로고    scopus 로고
    • Temporal dynamics of a two-neuron continuous network model with time delay
    • Majee, N.C., Roy, A.B.: Temporal dynamics of a two-neuron continuous network model with time delay. Appl. Math. Model. 21, 673-679 (1997)
    • (1997) Appl. Math. Model , vol.21 , pp. 673-679
    • Majee, N.C.1    Roy, A.B.2
  • 21
    • 33747980962 scopus 로고    scopus 로고
    • Stability switches and bifurcation analysis of a neural network with continuously delay
    • Liao, X.F., Wu, Z.F., Yu, J.B.: Stability switches and bifurcation analysis of a neural network with continuously delay. IEEE Trans. Syst. Man Cybernet. 29, 692-696 (1999)
    • (1999) IEEE Trans. Syst. Man Cybernet , vol.29 , pp. 692-696
    • Liao, X.F.1    Wu, Z.F.2    Yu, J.B.3
  • 22
    • 0035372163 scopus 로고    scopus 로고
    • Hopf bifurcation and chaos in a single delayed neuron equation with nonmonotonic activation function
    • Liao, X.F., Wong, K.W., Leung, C.S., Wu, Z.F.: Hopf bifurcation and chaos in a single delayed neuron equation with nonmonotonic activation function. Chaos Solitons Fractals 21, 1535-1547 (2001)
    • (2001) Chaos Solitons Fractals , vol.21 , pp. 1535-1547
    • Liao, X.F.1    Wong, K.W.2    Leung, C.S.3    Wu, Z.F.4
  • 23
    • 0035254276 scopus 로고    scopus 로고
    • Bifurcation analysis in a two-neuron system with distributed delays
    • Liao, X.F., Wong, K.W., Wu, Z.F.: Bifurcation analysis in a two-neuron system with distributed delays. Physica D 149, 123-141 (2001)
    • (2001) Physica D , vol.149 , pp. 123-141
    • Liao, X.F.1    Wong, K.W.2    Wu, Z.F.3
  • 24
    • 0037280036 scopus 로고    scopus 로고
    • Asymptotic stability criteria for a two-neuron network with different time delays
    • Liao, X.F., Wong, K.W., Wu, Z.F.: Asymptotic stability criteria for a two-neuron network with different time delays. IEEE Trans. Neural Network 14(1), 222-227 (2003)
    • (2003) IEEE Trans. Neural Network , vol.14 , Issue.1 , pp. 222-227
    • Liao, X.F.1    Wong, K.W.2    Wu, Z.F.3
  • 25
    • 0032165293 scopus 로고    scopus 로고
    • Robust interval stability analysis of Hopfield networks with time delays
    • Liao, X.F., Yu, J.B.: Robust interval stability analysis of Hopfield networks with time delays. IEEE Trans. Neural Network 9, 1042-1045 (1998)
    • (1998) IEEE Trans. Neural Network , vol.9 , pp. 1042-1045
    • Liao, X.F.1    Yu, J.B.2
  • 26
    • 0035508792 scopus 로고    scopus 로고
    • Novel robust stability criteria for interval delayed Hopfield neural networks with time delays
    • Liao, X.F., Wong, K.W., Wu, Z.F., Chen, G.: Novel robust stability criteria for interval delayed Hopfield neural networks with time delays. IEEE Tran. Syst. 148, 1355-1359 (2001)
    • (2001) IEEE Tran. Syst , vol.148 , pp. 1355-1359
    • Liao, X.F.1    Wong, K.W.2    Wu, Z.F.3    Chen, G.4
  • 27
    • 0035639130 scopus 로고    scopus 로고
    • Novel stability conditions for cellular neural networks with time delays
    • Liao, X.F., Yu, J.B., Chen, G.: Novel stability conditions for cellular neural networks with time delays. Int. J. Bif. Chaos 11(7), 1853-1864 (2001)
    • (2001) Int. J. Bif. Chaos , vol.11 , Issue.7 , pp. 1853-1864
    • Liao, X.F.1    Yu, J.B.2    Chen, G.3
  • 28
    • 0036647562 scopus 로고    scopus 로고
    • LMI-based approach for asymptotically stability analysis of delayed neural networks
    • Liao, X.F., Chen, G., Sanchez, E.N.: LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans. Circuits Syst. I 49, 1033-1039 (2002)
    • (2002) IEEE Trans. Circuits Syst. I , vol.49 , pp. 1033-1039
    • Liao, X.F.1    Chen, G.2    Sanchez, E.N.3
  • 29
    • 0036755232 scopus 로고    scopus 로고
    • Delay-dependent exponential stability analysis of delayed neural networks: An LMI approach
    • Liao, X.F., Chen, G., Sanchez, E.N.: Delay-dependent exponential stability analysis of delayed neural networks: An LMI approach. Neural Network 15, 855-866 (2002)
    • (2002) Neural Network , vol.15 , pp. 855-866
    • Liao, X.F.1    Chen, G.2    Sanchez, E.N.3
  • 30
    • 1942454843 scopus 로고    scopus 로고
    • Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain
    • Liao, X.F., Li, S.W., Chen, G.: Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain. Neural Network 17(4), 545-561 (2004)
    • (2004) Neural Network , vol.17 , Issue.4 , pp. 545-561
    • Liao, X.F.1    Li, S.W.2    Chen, G.3
  • 31
    • 1842587731 scopus 로고    scopus 로고
    • Liao, X.F., Wong, K.W.: Robust stability of interval bidirectional associative menmory neural networks with time delays. IEEE Trans. Man Cybernet. B 34(2), 1141-1154 (2004)
    • Liao, X.F., Wong, K.W.: Robust stability of interval bidirectional associative menmory neural networks with time delays. IEEE Trans. Man Cybernet. B 34(2), 1141-1154 (2004)
  • 32
    • 2342649582 scopus 로고    scopus 로고
    • Global exponential stability for a class of retarded functional differential equations with applications in neural networks
    • Liao, X.F., Wong, K.W.: Global exponential stability for a class of retarded functional differential equations with applications in neural networks. J. Math. Anal. Appl. 293(1), 125-148 (2004)
    • (2004) J. Math. Anal. Appl , vol.293 , Issue.1 , pp. 125-148
    • Liao, X.F.1    Wong, K.W.2
  • 33
    • 8444240791 scopus 로고    scopus 로고
    • Criteria for exponential stability of Cohen-Grossberg neural networks
    • Liao, X.F., Li, C.G., Wong, K.W.: Criteria for exponential stability of Cohen-Grossberg neural networks. Neural Network 17, 1401-1414 (2004)
    • (2004) Neural Network , vol.17 , pp. 1401-1414
    • Liao, X.F.1    Li, C.G.2    Wong, K.W.3
  • 34
    • 10444237980 scopus 로고    scopus 로고
    • Stability analysis for delayed cellular neural networks based on linear matrix inequality approach
    • Liao, X.F., Wong, K.W., Yang, S.Z.: Stability analysis for delayed cellular neural networks based on linear matrix inequality approach. Int. J. Bif. Chaos. 14(9), 3377-3384 (2004)
    • (2004) Int. J. Bif. Chaos , vol.14 , Issue.9 , pp. 3377-3384
    • Liao, X.F.1    Wong, K.W.2    Yang, S.Z.3
  • 35
    • 10844285334 scopus 로고    scopus 로고
    • An LMI approach to asymptotical stability of multi-delayed neural networks
    • Liao, X.F., Li, C.D.: An LMI approach to asymptotical stability of multi-delayed neural networks. Physica D 200(1-2), 139-155 (2005)
    • (2005) Physica D , vol.200 , Issue.1-2 , pp. 139-155
    • Liao, X.F.1    Li, C.D.2
  • 37
    • 0000046438 scopus 로고    scopus 로고
    • Transient oscillations in continuous-time excitatory ring neural networks with delay
    • Pakdaman, K., Malta, C.P., et al.: Transient oscillations in continuous-time excitatory ring neural networks with delay. Phys. Rev. E 55, 3234-3248 (1997)
    • (1997) Phys. Rev. E , vol.55 , pp. 3234-3248
    • Pakdaman, K.1    Malta, C.P.2
  • 38
    • 0032298907 scopus 로고    scopus 로고
    • Global attractivity in delayed Hopfield neural networks model
    • Van Den Driessche, P., Zou, X.: Global attractivity in delayed Hopfield neural networks model. SIAM J. Appl. Math. 58, 1878-1890 (1998)
    • (1998) SIAM J. Appl. Math , vol.58 , pp. 1878-1890
    • Van Den Driessche, P.1    Zou, X.2
  • 39
    • 0035890834 scopus 로고    scopus 로고
    • Bifurcations in a planar system of differential delay equations modeling neural activity
    • Giannakopoulos, F., Zapp, A.: Bifurcations in a planar system of differential delay equations modeling neural activity. Physica D 159(3-4), 215-232 (2001)
    • (2001) Physica D , vol.159 , Issue.3-4 , pp. 215-232
    • Giannakopoulos, F.1    Zapp, A.2
  • 40
    • 33646138961 scopus 로고    scopus 로고
    • Periodic solutions for a two-neuron network with delays
    • Liu, B., Huang, L.: Periodic solutions for a two-neuron network with delays. Nonlinear Anal. Real World Appl. 7(4), 497-509 (2006)
    • (2006) Nonlinear Anal. Real World Appl , vol.7 , Issue.4 , pp. 497-509
    • Liu, B.1    Huang, L.2
  • 41
    • 25844524957 scopus 로고    scopus 로고
    • Hopf bifurcation and chaos in Tabu learning neuron models
    • Li, C.G., Chen, G., Liao, X.F., Yu, J.B.: Hopf bifurcation and chaos in Tabu learning neuron models. Int. J. Bif. Chaos 15(8), 2633-2642 (2005)
    • (2005) Int. J. Bif. Chaos , vol.15 , Issue.8 , pp. 2633-2642
    • Li, C.G.1    Chen, G.2    Liao, X.F.3    Yu, J.B.4
  • 42
    • 0347130009 scopus 로고    scopus 로고
    • Stability and bifurcation in a neural network model with two delays
    • Wei, J., Ruan, S.: Stability and bifurcation in a neural network model with two delays. Physica D 130(1-2), 255-272 (1999)
    • (1999) Physica D , vol.130 , Issue.1-2 , pp. 255-272
    • Wei, J.1    Ruan, S.2


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