메뉴 건너뛰기




Volumn 89, Issue , 2012, Pages 193-201

Bogdanov-Takens bifurcation in a single inertial neuron model with delay

Author keywords

Bogdanov Takens bifurcation; Heteroclinic bifurcation; Homoclinic bifurcation; Inertial neuron model

Indexed keywords

BOGDANOV-TAKENS BIFURCATIONS; CENTER MANIFOLD REDUCTIONS; HETEROCLINIC BIFURCATIONS; HOMOCLINIC BIFURCATIONS; LIMIT CYCLE BIFURCATION; NEURON MODEL; NORM FORM; NORMAL FORM; PITCHFORK BIFURCATIONS; RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS; SADDLE NODE BIFURCATION; SINGLE NEURON;

EID: 84860246120     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2012.02.019     Document Type: Article
Times cited : (94)

References (18)
  • 3
    • 0000840165 scopus 로고
    • Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
    • Faria T., Magalhaes L.T. Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity. J. Differential Equations 1995, 122:201-224.
    • (1995) J. Differential Equations , vol.122 , pp. 201-224
    • Faria, T.1    Magalhaes, L.T.2
  • 4
    • 0000840164 scopus 로고
    • Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
    • Faria T., Magalhaes L.T. Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation. J. Differential Equations 1995, 122:181-200.
    • (1995) J. Differential Equations , vol.122 , pp. 181-200
    • Faria, T.1    Magalhaes, L.T.2
  • 6
    • 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. USA 1984, 81:3088.
    • (1984) Proc. Natl. Acad. Sci. USA , vol.81 , pp. 3088
    • Hopfield, J.J.1
  • 7
    • 84860251694 scopus 로고    scopus 로고
    • k,f in guinea-pig inner hair cells is regulated by protein kinase A
    • k,f in guinea-pig inner hair cells is regulated by protein kinase A. Neural Networks 2009, 22:1411-1418.
    • (2009) Neural Networks , vol.22 , pp. 1411-1418
    • Jagger, D.J.1    Ashmore, J.F.2
  • 8
    • 33947589642 scopus 로고    scopus 로고
    • Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback
    • Jiang W., Yuan Y. Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback. Physica D: Nonlinear Phenom. 2007, 227:149-161.
    • (2007) Physica D: Nonlinear Phenom. , vol.227 , pp. 149-161
    • Jiang, W.1    Yuan, Y.2
  • 11
    • 61749094363 scopus 로고    scopus 로고
    • Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation
    • Liu Q., Liao X., Guo S.T., Wu Y. Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation. Nonlinear Anal.: Real World Appl. 2009, 10:2384-2395.
    • (2009) Nonlinear Anal.: Real World Appl. , vol.10 , pp. 2384-2395
    • Liu, Q.1    Liao, X.2    Guo, S.T.3    Wu, Y.4
  • 12
    • 70450237939 scopus 로고    scopus 로고
    • Dynamics of an inertial two-neuron system with time delay
    • Liu Q., Liao X., Liu Y., Zhou S., Guo S.T. Dynamics of an inertial two-neuron system with time delay. Nonlinear Dyn. 2009, 58:573-609.
    • (2009) Nonlinear Dyn. , vol.58 , pp. 573-609
    • Liu, Q.1    Liao, X.2    Liu, Y.3    Zhou, S.4    Guo, S.T.5
  • 13
    • 0000256610 scopus 로고
    • Stability of analog neural networks with delay
    • Marcus C., Westervelt R. Stability of analog neural networks with delay. Phys. Rev. A 1989, 39:347-359.
    • (1989) Phys. Rev. A , vol.39 , pp. 347-359
    • Marcus, C.1    Westervelt, R.2
  • 14
    • 84874775369 scopus 로고    scopus 로고
    • Evidence of a Hopf bifurcation in frog hair cells
    • Ospeck M., Eguiluz V., Magnasco M. Evidence of a Hopf bifurcation in frog hair cells. Biophys. J. 2001, 80:2597-2607.
    • (2001) Biophys. J. , vol.80 , pp. 2597-2607
    • Ospeck, M.1    Eguiluz, V.2    Magnasco, M.3
  • 15
    • 0030164858 scopus 로고    scopus 로고
    • Model-based learning for mobile robot navigation from the dynamical systems perspective
    • Tani J. Model-based learning for mobile robot navigation from the dynamical systems perspective. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 1996, 26:421-436.
    • (1996) IEEE Trans. Syst. Man Cybern. Part B: Cybern. , vol.26 , pp. 421-436
    • Tani, J.1
  • 16
    • 22244461346 scopus 로고
    • Coupling of memory search and mental rotation by a nonequilibrium dynamics neural network
    • Tani J., Fujita M. Coupling of memory search and mental rotation by a nonequilibrium dynamics neural network. IEEE Trans. Fundam. Electron. Commun. Comput. Sci. 1992, 75:578-585.
    • (1992) IEEE Trans. Fundam. Electron. Commun. Comput. Sci. , vol.75 , pp. 578-585
    • Tani, J.1    Fujita, M.2
  • 17
    • 0038537695 scopus 로고    scopus 로고
    • Stability and chaos in an inertial two-neuron system
    • Wheeler D.W., Schieve W.C. Stability and chaos in an inertial two-neuron system. Physica D: Nonlinear Phenom. 1997, 105:267-284.
    • (1997) Physica D: Nonlinear Phenom. , vol.105 , pp. 267-284
    • Wheeler, D.W.1    Schieve, W.C.2
  • 18
    • 37149008019 scopus 로고    scopus 로고
    • Homoclinic orbits and Hopf bifurcations in delay differential systems with TB singularity
    • Xu Y., Huang M. Homoclinic orbits and Hopf bifurcations in delay differential systems with TB singularity. J. Differential Equations 2008, 244:582-598.
    • (2008) J. Differential Equations , vol.244 , pp. 582-598
    • Xu, Y.1    Huang, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.