메뉴 건너뛰기




Volumn 216, Issue 2, 2010, Pages 631-646

Dynamics of a delayed two-coupled oscillator with excitatory-to-excitatory connection

Author keywords

Equilibria; Hopf bifurcation; Oscillator; Stability

Indexed keywords

CENTER MANIFOLD REDUCTIONS; CHARACTERISTIC EQUATION; COUPLED OSCILLATORS; DELAY DIFFERENTIAL EQUATIONS; DELAYED FEEDBACK; LIE GROUP; LINEAR STABILITY; LINEARIZED SYSTEMS; NEURAL NETWORK MODEL; NORMAL FORM THEORY; NUMERICAL SIMULATION; OSCILLATOR STABILITY; PARAMETER SPACES; PERIODIC OSCILLATION; PERIODIC SOLUTION; REPRESENTATION THEORY; SPATIOTEMPORAL PATTERNS; STABILITY AND BIFURCATION; SYMMETRIC BIFURCATION; THEORETICAL RESULT;

EID: 77649236542     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.01.097     Document Type: Article
Times cited : (9)

References (27)
  • 1
    • 22244473030 scopus 로고    scopus 로고
    • Delay induced periodicity in a neural netlet of excitation and inhibition
    • Gopalsamy K., and 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
  • 2
    • 0347130009 scopus 로고    scopus 로고
    • Stability and bifurcation in a neural network model with two delays
    • Wei J., and Ruan S. Stability and bifurcation in a neural network model with two delays. Physica D 130 (1999) 255-272
    • (1999) Physica D , vol.130 , pp. 255-272
    • Wei, J.1    Ruan, S.2
  • 3
    • 0001082564 scopus 로고    scopus 로고
    • Bifurcations, stability and monotonicity properties of a delayed neural network model
    • Olien L., and Bélair J. Bifurcations, stability and monotonicity properties of a delayed neural network model. Physica D 102 (1997) 349-363
    • (1997) Physica D , vol.102 , pp. 349-363
    • Olien, L.1    Bélair, J.2
  • 4
    • 0038346772 scopus 로고    scopus 로고
    • Existence and attraction of a phase-locked oscillation in a delayed network of two neurons
    • Chen Y., and Wu J. Existence and attraction of a phase-locked oscillation in a delayed network of two neurons. Differ. Integral Eqs. 14 (2001) 1181-1236
    • (2001) Differ. Integral Eqs. , vol.14 , pp. 1181-1236
    • Chen, Y.1    Wu, J.2
  • 5
    • 36849021007 scopus 로고    scopus 로고
    • Two-parameter bifurcations in a network of two neurons with multiple delays
    • Guo S., Chen Y., and Wu J. Two-parameter bifurcations in a network of two neurons with multiple delays. J. Differ. Eqs. 244 (2008) 444-486
    • (2008) J. Differ. Eqs. , vol.244 , pp. 444-486
    • Guo, S.1    Chen, Y.2    Wu, J.3
  • 6
    • 4944247888 scopus 로고    scopus 로고
    • Linear stability and Hopf bifurcation in a two-neuron network with three delays
    • Guo S., Huang L., and Wang L. Linear stability and Hopf bifurcation in a two-neuron network with three delays. Int. J. Bifur. Chaos Appl. Sci. Eng. 14 (2004) 2799-2810
    • (2004) Int. J. Bifur. Chaos Appl. Sci. Eng. , vol.14 , pp. 2799-2810
    • Guo, S.1    Huang, L.2    Wang, L.3
  • 7
    • 19944411214 scopus 로고    scopus 로고
    • Regular dynamics in a delayed network of two neurons with all-or-none activation functions
    • Guo S., Huang L., and Wu J. Regular dynamics in a delayed network of two neurons with all-or-none activation functions. Physica D 206 (2005) 32-48
    • (2005) Physica D , vol.206 , pp. 32-48
    • Guo, S.1    Huang, L.2    Wu, J.3
  • 8
    • 22144455717 scopus 로고    scopus 로고
    • Hopf bifurcation of a two-neuron network with different discrete time delays
    • Li S., Liao X., Li C., and Wong K.-W. Hopf bifurcation of a two-neuron network with different discrete time delays. Int. J. Bifur. Chaos Appl. Sci. Eng. 15 (2005) 1589-1601
    • (2005) Int. J. Bifur. Chaos Appl. Sci. Eng. , vol.15 , pp. 1589-1601
    • Li, S.1    Liao, X.2    Li, C.3    Wong, K.-W.4
  • 9
    • 0031276105 scopus 로고    scopus 로고
    • Temporal dynamics of a two-neuron continuous network model with time delay
    • Majee N.C., and Roy A.B. Temporal dynamics of a two-neuron continuous network model with time delay. Appl. Math. Modell. 21 (1997) 673-679
    • (1997) Appl. Math. Modell. , vol.21 , pp. 673-679
    • Majee, N.C.1    Roy, A.B.2
  • 10
    • 0342936163 scopus 로고    scopus 로고
    • Stability, bifurcation, and multistability in a system of two-coupled neurons with multiple time delays
    • Shayer L., and Campbell S. Stability, bifurcation, and multistability in a system of two-coupled neurons with multiple time delays. SIAM J. Appl. Math. 61 (2000) 673-700
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 673-700
    • Shayer, L.1    Campbell, S.2
  • 11
    • 0038381865 scopus 로고    scopus 로고
    • Nonlinear waves in networks of neurons with delayed feedback: pattern formation and continuation
    • Huang L., and Wu J. Nonlinear waves in networks of neurons with delayed feedback: pattern formation and continuation. SIAM J. Math. Anal. 34 (2003) 836-860
    • (2003) SIAM J. Math. Anal. , vol.34 , pp. 836-860
    • Huang, L.1    Wu, J.2
  • 12
    • 6444228136 scopus 로고    scopus 로고
    • Global existence of periodic solutions in a tri-neuron network model with delays
    • Wei J., and Li M.Y. Global existence of periodic solutions in a tri-neuron network model with delays. Physica D 198 (2004) 106-119
    • (2004) Physica D , vol.198 , pp. 106-119
    • Wei, J.1    Li, M.Y.2
  • 13
    • 33646864830 scopus 로고    scopus 로고
    • Symmetric functional differential equations and neural networks with memory
    • Wu J. Symmetric functional differential equations and neural networks with memory. Trans. Amer. Math. Soc. 350 (1998) 4799-4838
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 4799-4838
    • Wu, J.1
  • 14
    • 33746239186 scopus 로고    scopus 로고
    • Hopf bifurcation and stability for a delayed tri-neuron neural network model
    • Yan X. Hopf bifurcation and stability for a delayed tri-neuron neural network model. J. Comput. Appl. Math. 196 (2006) 579-595
    • (2006) J. Comput. Appl. Math. , vol.196 , pp. 579-595
    • Yan, X.1
  • 15
    • 45149139481 scopus 로고
    • Amplitude response of coupled oscillators
    • Aronson D., Ermentrout G.B., and Kopell N. Amplitude response of coupled oscillators. Physica D 41 (1990) 403-449
    • (1990) Physica D , vol.41 , pp. 403-449
    • Aronson, D.1    Ermentrout, G.B.2    Kopell, N.3
  • 16
    • 33846421760 scopus 로고
    • Multiple pulse interactions and averaging in systems of coupled neural oscillators
    • Ermentrout G.B., and Kopell N. Multiple pulse interactions and averaging in systems of coupled neural oscillators. J. Math. Biol. 29 (1991) 195-217
    • (1991) J. Math. Biol. , vol.29 , pp. 195-217
    • Ermentrout, G.B.1    Kopell, N.2
  • 17
    • 0018700693 scopus 로고
    • Synergism and antagonism of neurons caused by an electrical synapse
    • Kawato M., Sokabe M., and Suzuki R. Synergism and antagonism of neurons caused by an electrical synapse. Biol. Cybern. 34 (1979) 81-89
    • (1979) Biol. Cybern. , vol.34 , pp. 81-89
    • Kawato, M.1    Sokabe, M.2    Suzuki, R.3
  • 18
    • 0020049721 scopus 로고
    • A model of the nerve impulse using two first-order differential equations
    • Hindmarsh J.L., and Rose R.M. A model of the nerve impulse using two first-order differential equations. Nature 296 (1982) 162-164
    • (1982) Nature , vol.296 , pp. 162-164
    • Hindmarsh, J.L.1    Rose, R.M.2
  • 19
    • 21144480274 scopus 로고
    • Phase dynamics for weakly coupled Hodgkin-Huxley neurons
    • Hansel D., Mato G., and Meunier C. Phase dynamics for weakly coupled Hodgkin-Huxley neurons. Europhys. Lett. 23 (1993) 367-372
    • (1993) Europhys. Lett. , vol.23 , pp. 367-372
    • Hansel, D.1    Mato, G.2    Meunier, C.3
  • 20
    • 0015260274 scopus 로고
    • Excitatory and inhibitory interactions in localized populations of model neurons
    • Wilson H.R., and Cowan J.D. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12 (1972) 1-24
    • (1972) Biophys. J. , vol.12 , pp. 1-24
    • Wilson, H.R.1    Cowan, J.D.2
  • 23
    • 5644291545 scopus 로고
    • Complex dynamics in simple neural circuits
    • Denker J.S. (Ed), American Institute of Physics, New York
    • Babcock K.L., and Westervelt R.M. Complex dynamics in simple neural circuits. In: Denker J.S. (Ed). Neural Networks for Computing (1986), American Institute of Physics, New York 288-293
    • (1986) Neural Networks for Computing , pp. 288-293
    • Babcock, K.L.1    Westervelt, R.M.2
  • 24
    • 0012869306 scopus 로고
    • Dynamics of simple electronic neural networks with added inertia
    • Babcock K.L., and Westervelt R.M. Dynamics of simple electronic neural networks with added inertia. Physica D 23 (1987) 464-469
    • (1987) Physica D , vol.23 , pp. 464-469
    • Babcock, K.L.1    Westervelt, R.M.2
  • 25
    • 67650711301 scopus 로고    scopus 로고
    • Equivariant hopf bifurcation for neutral functional differential equations
    • Guo S., and Lamb J.S.W. Equivariant hopf bifurcation for neutral functional differential equations. Proc. Amer. Math. Soc. 136 (2008) 2031-2041
    • (2008) Proc. Amer. Math. Soc. , vol.136 , pp. 2031-2041
    • Guo, S.1    Lamb, J.S.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.