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Volumn 17, Issue 4, 2007, Pages 1355-1366

Stability and hopf bifurcation on a two-neuron system with time delay in the frequency domain

Author keywords

Graphic Hopf bifurcation theorem; Harmonic balance; Hopf bifurcation; Nyquist criterion; Periodic solutions; Time delay

Indexed keywords

FREQUENCY DOMAIN ANALYSIS; NUMERICAL METHODS; PARAMETER ESTIMATION; SYSTEM STABILITY; THEOREM PROVING; TIME DELAY;

EID: 34250216025     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127407017859     Document Type: Article
Times cited : (24)

References (36)
  • 1
    • 84971124048 scopus 로고
    • Harmonic balance and the Hopf bifurcation theorem
    • Allwright, D. J. [1977] "Harmonic balance and the Hopf bifurcation theorem," Math. Proc. Camb. Philosph. Soc. 82, 453-467.
    • (1977) Math. Proc. Camb. Philosph. Soc , vol.82 , pp. 453-467
    • Allwright, D.J.1
  • 2
    • 0023435167 scopus 로고
    • Dynamics of simple electronic neural networks
    • Babcock, K. L. & Westervelt, R. M. [1987] "Dynamics of simple electronic neural networks," Physica D 28, 305-316.
    • (1987) Physica D , vol.28 , pp. 305-316
    • Babcock, K.L.1    Westervelt, R.M.2
  • 3
    • 0028468031 scopus 로고
    • How delays affect neural dynamics and learning
    • Baldi, P. & Atiya, A. [1994] "How delays affect neural dynamics and learning," IEEE Trans. Neural Networks 5, 612-621.
    • (1994) IEEE Trans. Neural Networks , vol.5 , pp. 612-621
    • Baldi, P.1    Atiya, A.2
  • 4
    • 2442484035 scopus 로고    scopus 로고
    • Globally exponentially robust stability and periodicity of delayed neural networks
    • Cao, J. & Chen, T. [2004] "Globally exponentially robust stability and periodicity of delayed neural networks," Chaos Solit. Fract. 22, 957-963.
    • (2004) Chaos Solit. Fract , vol.22 , pp. 957-963
    • Cao, J.1    Chen, T.2
  • 5
    • 3442880393 scopus 로고    scopus 로고
    • Boundedness and stability for Cohen-Grossberg neural network with time-varying delays
    • Cao, J. & Liang, J. [2004] "Boundedness and stability for Cohen-Grossberg neural network with time-varying delays," J. Math. Anal. Appl. 296, 665-685.
    • (2004) J. Math. Anal. Appl , vol.296 , pp. 665-685
    • Cao, J.1    Liang, J.2
  • 6
    • 10644236158 scopus 로고    scopus 로고
    • Exponential stability of high-order bidirectional associative memory neural networks with time delays
    • Cao, J., Liang, J. & Lam, J. [2004] "Exponential stability of high-order bidirectional associative memory neural networks with time delays," Physica D 199, 425-436.
    • (2004) Physica D , vol.199 , pp. 425-436
    • Cao, J.1    Liang, J.2    Lam, J.3
  • 7
    • 1642287604 scopus 로고    scopus 로고
    • Absolute exponential stability of recurrent neural networks with Lipschitzcontinuous activation functions and time delays
    • Cao, J. & Wang, J. [2004] "Absolute exponential stability of recurrent neural networks with Lipschitzcontinuous activation functions and time delays," Neural Networks 17, 379-390.
    • (2004) Neural Networks , vol.17 , pp. 379-390
    • Cao, J.1    Wang, J.2
  • 8
    • 3142672983 scopus 로고    scopus 로고
    • Global robust stability of delayed recurrent neural networks
    • Cao, J., Huang, D. & Qu, Y. [2005] "Global robust stability of delayed recurrent neural networks," Chaos Solit. Fract. 23, 221-229.
    • (2005) Chaos Solit. Fract , vol.23 , pp. 221-229
    • Cao, J.1    Huang, D.2    Qu, Y.3
  • 9
    • 27744450164 scopus 로고    scopus 로고
    • Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach
    • Cao, J. & Li, X. [2005] "Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach," Physica D 212, 54-65.
    • (2005) Physica D , vol.212 , pp. 54-65
    • Cao, J.1    Li, X.2
  • 10
    • 14644434391 scopus 로고    scopus 로고
    • Cao, J. & Wang, J. [2005] Global asymptotic and robust stability of recurrent neural networks with time delays, IEEE Trans. Circuits Syst.-152, 417-426.
    • Cao, J. & Wang, J. [2005] "Global asymptotic and robust stability of recurrent neural networks with time delays," IEEE Trans. Circuits Syst.-152, 417-426.
  • 11
    • 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
  • 12
    • 0031101884 scopus 로고    scopus 로고
    • Convergence under dynamical thresholds with delays
    • Gopalsamy, K. & Leung, I. [1997] "Convergence under dynamical thresholds with delays," IEEE Trans. Neural Networks 8, 341-348.
    • (1997) IEEE Trans. Neural Networks , vol.8 , pp. 341-348
    • Gopalsamy, K.1    Leung, I.2
  • 13
    • 4944247888 scopus 로고    scopus 로고
    • Linear stability and Hopf bifurcation in a two-neuron network with three delays
    • Guo, S., Huang, L. & Wang, L. [2004] "Linear stability and Hopf bifurcation in a two-neuron network with three delays," Int. J. Bifurcation and Chaos 14, 2799-2810.
    • (2004) Int. J. Bifurcation and Chaos , vol.14 , pp. 2799-2810
    • Guo, S.1    Huang, L.2    Wang, L.3
  • 15
    • 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
  • 16
    • 0023861743 scopus 로고
    • Bi-directional associative memories
    • Kosko, B. [1988] "Bi-directional associative memories," IEEE Trans. Syst. Man Cybern. 18, 49-60.
    • (1988) IEEE Trans. Syst. Man Cybern , vol.18 , pp. 49-60
    • Kosko, B.1
  • 17
    • 33747980962 scopus 로고    scopus 로고
    • Stability switches and bifurcation analysis of a neural network with continuously delay
    • Liao, X., Wu, Z. & Yu, J. [1999] "Stability switches and bifurcation analysis of a neural network with continuously delay," IEEE Trans. Syst. Man Cybern. 29, 692-696.
    • (1999) IEEE Trans. Syst. Man Cybern , vol.29 , pp. 692-696
    • Liao, X.1    Wu, Z.2    Yu, J.3
  • 18
    • 0035466085 scopus 로고    scopus 로고
    • Hopf bifurcation and stability of periodic solutions for van der Pol equation with distributed delay
    • Liao, X., Wong, K. & Wu, Z. [2001a] "Hopf bifurcation and stability of periodic solutions for van der Pol equation with distributed delay," Nonlin. Dyn. 26, 23-44.
    • (2001) Nonlin. Dyn , vol.26 , pp. 23-44
    • Liao, X.1    Wong, K.2    Wu, Z.3
  • 19
    • 0035254276 scopus 로고    scopus 로고
    • Bifurcation analysis in a two-neuron system with distributed delay
    • Liao, X., Wong, K. & Wu, Z. [2001b] "Bifurcation analysis in a two-neuron system with distributed delay," Physica D 149, 123-141.
    • (2001) Physica D , vol.149 , pp. 123-141
    • Liao, X.1    Wong, K.2    Wu, Z.3
  • 20
    • 0017450097 scopus 로고
    • The generalized Nyquist stability criterion and multivariable root loci
    • MacFarlane, A. G. J. & Postlethwaite, I. [1977] "The generalized Nyquist stability criterion and multivariable root loci," Int. J. Contr. 25, 81-127.
    • (1977) Int. J. Contr , vol.25 , pp. 81-127
    • MacFarlane, A.G.J.1    Postlethwaite, I.2
  • 21
    • 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
  • 22
    • 0018452921 scopus 로고
    • The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems
    • Mees, A. I. & Chua, L. O. [1979] "The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems," IEEE Trans. Circuits Syst. 26, 235-254.
    • (1979) IEEE Trans. Circuits Syst , vol.26 , pp. 235-254
    • Mees, A.I.1    Chua, L.O.2
  • 24
    • 0027593222 scopus 로고
    • Computation of limit cycles via higher-order harmonic balance approximation
    • Moiola, J. L. & Chen, G. [1993a] "Computation of limit cycles via higher-order harmonic balance approximation," IEEE Trans. Autom. Contr. 38, 782-790.
    • (1993) IEEE Trans. Autom. Contr , vol.38 , pp. 782-790
    • Moiola, J.L.1    Chen, G.2
  • 25
    • 21344496839 scopus 로고
    • Frequency domain approach to computation and analysis of bifurcations and limit cycles: A tutorial
    • Moiola, J. L. & Chen, G. [1993b] "Frequency domain approach to computation and analysis of bifurcations and limit cycles: A tutorial," Int. J. Bifurcation and Chaos 3, 843-867.
    • (1993) Int. J. Bifurcation and Chaos , vol.3 , pp. 843-867
    • Moiola, J.L.1    Chen, G.2
  • 27
    • 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
  • 28
    • 0035011952 scopus 로고    scopus 로고
    • On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion
    • Ruan, S. & Wei, J. [2001] "On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion," IMA J. Math. Appl. Med. Biol. 18, 41-52.
    • (2001) IMA J. Math. Appl. Med. Biol , vol.18 , pp. 41-52
    • Ruan, S.1    Wei, J.2
  • 29
    • 1842465386 scopus 로고    scopus 로고
    • On the zeros of transcendental functions with applications to stability of delay differential equations with two delays
    • Ruan, S. & Wei, J. [2003] "On the zeros of transcendental functions with applications to stability of delay differential equations with two delays," Dyn. Contin. Discr. Impuls. Syst. Ser. A Math. Anal. 10, 863-874.
    • (2003) Dyn. Contin. Discr. Impuls. Syst. Ser. A Math. Anal , vol.10 , pp. 863-874
    • Ruan, S.1    Wei, J.2
  • 30
    • 12244261643 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays
    • Song, Y., Han, M. & Wei, J. [2005] "Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays," Physica D 200, 185-204.
    • (2005) Physica D , vol.200 , pp. 185-204
    • Song, Y.1    Han, M.2    Wei, J.3
  • 31
    • 10144242643 scopus 로고    scopus 로고
    • Local Hopf bifurcation and global periodic solutions in a delayed predator-prey system
    • Song, Y. & Wei, J. [2005] "Local Hopf bifurcation and global periodic solutions in a delayed predator-prey system," J. Math. Anal. Appl. 301, 1-21.
    • (2005) J. Math. Anal. Appl , vol.301 , pp. 1-21
    • Song, Y.1    Wei, J.2
  • 32
    • 0039260015 scopus 로고
    • Stability of systems with delayed feedback
    • Tsypkin, Y. [1946] "Stability of systems with delayed feedback," Automat. Telemekh 7, 107-129;
    • (1946) Automat. Telemekh , vol.7 , pp. 107-129
    • Tsypkin, Y.1
  • 33
    • 34250159336 scopus 로고    scopus 로고
    • Also reprinted in MacFarlane, A. G. J. (ed.) [1979] Frequency Response Methods in Control Systems (IEEE Press), pp. 45-56.
    • Also reprinted in MacFarlane, A. G. J. (ed.) [1979] Frequency Response Methods in Control Systems (IEEE Press), pp. 45-56.
  • 34
    • 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 D 130, 255-272.
    • (1999) Physica D , vol.130 , pp. 255-272
    • Wei, J.1    Ruan, S.2
  • 35
    • 18444371144 scopus 로고    scopus 로고
    • Hopf bifurcation and stability of periodic solutions for van der Pol equation with time delay
    • Yu, W. & Cao, J. [2005] "Hopf bifurcation and stability of periodic solutions for van der Pol equation with time delay," Nonlin. Anal. 62, 141-165.
    • (2005) Nonlin. Anal , vol.62 , pp. 141-165
    • Yu, W.1    Cao, J.2
  • 36
    • 31744442908 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays
    • Yu, W. & Cao, J. [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.1    Cao, J.2


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