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Volumn 238, Issue 23-24, 2009, Pages 2409-2418

Bifurcation and stabilization of oscillations in ring neural networks with inertia

Author keywords

Bifurcation; Inertia; Kinematical model; Ring neural network; Traveling wave

Indexed keywords

BIFURCATION (MATHEMATICS); CIRCUIT OSCILLATIONS; NEURAL NETWORKS; NEURONS;

EID: 70350569944     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2009.09.021     Document Type: Article
Times cited : (29)

References (47)
  • 1
    • 0028166567 scopus 로고
    • A group-theoretic approach to rings of coupled biological oscillators
    • Collins J.J., and Stewart I. A group-theoretic approach to rings of coupled biological oscillators. Biol. Cybernet. 71 (1994) 95-103
    • (1994) Biol. Cybernet. , vol.71 , pp. 95-103
    • Collins, J.J.1    Stewart, I.2
  • 2
    • 0029847273 scopus 로고    scopus 로고
    • Principles of rhythmic motor pattern production
    • Marder E., and Calabrese R.L. Principles of rhythmic motor pattern production. Physiol. Rev. 76 (1996) 687-717
    • (1996) Physiol. Rev. , vol.76 , pp. 687-717
    • Marder, E.1    Calabrese, R.L.2
  • 4
    • 0024909476 scopus 로고
    • Convergent activation dynamics in continuous time networks
    • Hirsh M.H. Convergent activation dynamics in continuous time networks. Neural Netw. 2 (1989) 331-340
    • (1989) Neural Netw. , vol.2 , pp. 331-340
    • Hirsh, M.H.1
  • 5
    • 0000913896 scopus 로고
    • Oscillations and synchronizations in neural networks: An exploration of the labeling hypothesis
    • Atiya A.F., and Baldi P. Oscillations and synchronizations in neural networks: An exploration of the labeling hypothesis. Int. J. Neural Syst. 1 (1989) 103-124
    • (1989) Int. J. Neural Syst. , vol.1 , pp. 103-124
    • Atiya, A.F.1    Baldi, P.2
  • 7
    • 0029064165 scopus 로고
    • Characterization of periodic attractors in neural ring networks
    • Pasemann F. Characterization of periodic attractors in neural ring networks. Neural Netw. 8 (1995) 421-429
    • (1995) Neural Netw. , vol.8 , pp. 421-429
    • Pasemann, F.1
  • 8
    • 34247111800 scopus 로고    scopus 로고
    • Pattern formation and continuation in a trineuron ring with delays
    • Guo S., and Huang L. Pattern formation and continuation in a trineuron ring with delays. Acta Math. Sin. 23 (2007) 799-818
    • (2007) Acta Math. Sin. , vol.23 , pp. 799-818
    • Guo, S.1    Huang, L.2
  • 9
    • 38049039264 scopus 로고    scopus 로고
    • Complicated dynamics of a ring neural network with time delays
    • (23pp)
    • Xu X. Complicated dynamics of a ring neural network with time delays. J. Phys. A 41 (2008) 035102 (23pp)
    • (2008) J. Phys. A , vol.41 , pp. 035102
    • Xu, X.1
  • 10
    • 0023435167 scopus 로고
    • Dynamics of simple electronic neural networks
    • Babcock K.L., and Westervelt R.M. Dynamics of simple electronic neural networks. Physica D 28 (1987) 305-316
    • (1987) Physica D , vol.28 , pp. 305-316
    • Babcock, K.L.1    Westervelt, R.M.2
  • 11
    • 0028468031 scopus 로고
    • How delays affect neural dynamics and learning
    • Baldi P., and Atiya A.F. How delays affect neural dynamics and learning. IEEE Trans. Neural Netw. 5 (1994) 612-621
    • (1994) IEEE Trans. Neural Netw. , vol.5 , pp. 612-621
    • Baldi, P.1    Atiya, A.F.2
  • 12
    • 0000046438 scopus 로고    scopus 로고
    • Transient oscillations in continuous-time excitatory ring neural networks with delay
    • Pakdaman K., Malta C.P., Grotta-Ragazzo C., Arino O., and Vibert J.-F. Transient oscillations in continuous-time excitatory ring neural networks with delay. Phys. Rev. E 55 (1997) 3234-3248
    • (1997) Phys. Rev. E , vol.55 , pp. 3234-3248
    • Pakdaman, K.1    Malta, C.P.2    Grotta-Ragazzo, C.3    Arino, O.4    Vibert, J.-F.5
  • 14
    • 70350575078 scopus 로고    scopus 로고
    • T. Ishii, H. Kitajima, Oscillation in cyclic coupled neurons, in: Proc. 2006 RISP Int. Workshop on Nonlinear Circuits and Signal Processing, NCSP2006, 2006, pp. 97-100
    • T. Ishii, H. Kitajima, Oscillation in cyclic coupled neurons, in: Proc. 2006 RISP Int. Workshop on Nonlinear Circuits and Signal Processing, NCSP2006, 2006, pp. 97-100
  • 18
    • 58149142989 scopus 로고    scopus 로고
    • Duration of transient oscillations in ring networks of unidirectionally coupled neurons
    • Horikawa Y., and Kitajima H. Duration of transient oscillations in ring networks of unidirectionally coupled neurons. Physica D 238 (2009) 216-225
    • (2009) Physica D , vol.238 , pp. 216-225
    • Horikawa, Y.1    Kitajima, H.2
  • 19
    • 67650450880 scopus 로고    scopus 로고
    • Mechanism of long transient oscillations in cyclic coupled systems
    • Kitajima H., and Horikawa Y. Mechanism of long transient oscillations in cyclic coupled systems. Chaos Solitons Fractals (2009) 1854-1859
    • (2009) Chaos Solitons Fractals , pp. 1854-1859
    • Kitajima, H.1    Horikawa, Y.2
  • 20
    • 49049141478 scopus 로고
    • Kink dynamics in one-dimensional nonlinear systems
    • Kawasaki K., and Ohta T. Kink dynamics in one-dimensional nonlinear systems. Physica 116A (1982) 573-593
    • (1982) Physica , vol.116 A , pp. 573-593
    • Kawasaki, K.1    Ohta, T.2
  • 21
    • 84990619184 scopus 로고
    • Metastable patterns in solutions of u = ε u - f (u)
    • Carr J., and Pego R.L. Metastable patterns in solutions of u = ε u - f (u). Comm. Pure Appl. Math. 42 (1989) 523-576
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 523-576
    • Carr, J.1    Pego, R.L.2
  • 22
    • 0000400648 scopus 로고
    • Equation of motion for interacting pulses
    • Ei S., and Ohta T. Equation of motion for interacting pulses. Phys. Rev. E 50 (1994) 4672-4678
    • (1994) Phys. Rev. E , vol.50 , pp. 4672-4678
    • Ei, S.1    Ohta, T.2
  • 23
    • 58149239838 scopus 로고    scopus 로고
    • Duration of transient fronts in a bistable reaction-diffusion equation in a one-dimensional bounded domain
    • Horikawa Y. Duration of transient fronts in a bistable reaction-diffusion equation in a one-dimensional bounded domain. Phy. Rev. E 78 (2008) 066108/1-066108/10
    • (2008) Phy. Rev. E , vol.78
    • Horikawa, Y.1
  • 24
    • 0030269055 scopus 로고    scopus 로고
    • Metastable bubble solutions for the Allen-Cahn equation with mass conservation
    • Ward M.J. Metastable bubble solutions for the Allen-Cahn equation with mass conservation. SIAM J. Appl. Math. 56 (1996) 1247-1279
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 1247-1279
    • Ward, M.J.1
  • 25
    • 0041010982 scopus 로고    scopus 로고
    • Dynamic metastability and singular perturbations
    • Boundaries, Interfaces, and Transitions. Delfour M.C. (Ed), AMS
    • Ward M.J. Dynamic metastability and singular perturbations. In: Delfour M.C. (Ed). Boundaries, Interfaces, and Transitions. CRM Proceedings and Lecture Notes vol. 13 (1998), AMS 237-263
    • (1998) CRM Proceedings and Lecture Notes , vol.13 , pp. 237-263
    • Ward, M.J.1
  • 26
    • 5344273683 scopus 로고
    • Supertransients, spatiotemporal intermittency and stability of fully developed spatiotemporal chaos
    • Kaneko K. Supertransients, spatiotemporal intermittency and stability of fully developed spatiotemporal chaos. Phys. Lett. A 149 (1990) 105-112
    • (1990) Phys. Lett. A , vol.149 , pp. 105-112
    • Kaneko, K.1
  • 27
    • 71849091229 scopus 로고
    • Transient spatio-temporal chaos in a reaction-diffusion model
    • Wacker A., Bose S., and Schöll E. Transient spatio-temporal chaos in a reaction-diffusion model. Europhys. Lett. 31 (1995) 257-262
    • (1995) Europhys. Lett. , vol.31 , pp. 257-262
    • Wacker, A.1    Bose, S.2    Schöll, E.3
  • 28
    • 34247465930 scopus 로고    scopus 로고
    • Desynchronized stable states in diluted neural networks
    • Zillmera R., Livib R., Politic A., and Torcini A. Desynchronized stable states in diluted neural networks. Neurocomputing 70 (2007) 1960-1965
    • (2007) Neurocomputing , vol.70 , pp. 1960-1965
    • Zillmera, R.1    Livib, R.2    Politic, A.3    Torcini, A.4
  • 29
    • 0032557371 scopus 로고    scopus 로고
    • Relaxation, closing probabilities and transition from oscillatory to chaotic attractors in asymmetric neural networks
    • Bastolla U., and Parisi G. Relaxation, closing probabilities and transition from oscillatory to chaotic attractors in asymmetric neural networks. J. Phys. A 31 (1998) 4583-4602
    • (1998) J. Phys. A , vol.31 , pp. 4583-4602
    • Bastolla, U.1    Parisi, G.2
  • 30
    • 0041888472 scopus 로고    scopus 로고
    • Exponential transients in continuous-time Liapunov systems
    • Šíma J., and Orponen P. Exponential transients in continuous-time Liapunov systems. Theoret. Comput. Sci. 306 (2003) 353-372
    • (2003) Theoret. Comput. Sci. , vol.306 , pp. 353-372
    • Šíma, J.1    Orponen, P.2
  • 31
    • 0012869306 scopus 로고
    • Stability and dynamics of simple electronic neural networks with added inertia
    • Babcock K.L., and Westervelt R.M. Stability and dynamics of simple electronic neural networks with added inertia. Physica D 23 (1986) 464-469
    • (1986) Physica D , vol.23 , pp. 464-469
    • Babcock, K.L.1    Westervelt, R.M.2
  • 32
    • 0038537695 scopus 로고    scopus 로고
    • Stability and chaos in an inertial two-neuron system
    • Wheeler D.W., and Schieve W.C. Stability and chaos in an inertial two-neuron system. Physica D 105 (1997) 267-284
    • (1997) Physica D , vol.105 , pp. 267-284
    • Wheeler, D.W.1    Schieve, W.C.2
  • 35
    • 53349102813 scopus 로고
    • Impulse and physiological states in theoretical models of nerve membrane
    • FitzHugh R. Impulse and physiological states in theoretical models of nerve membrane. Biophys. J. 1 (1961) 445-466
    • (1961) Biophys. J. , vol.1 , pp. 445-466
    • FitzHugh, R.1
  • 36
    • 6344238035 scopus 로고
    • An active pulse transmission line simulating nerve axon
    • Nagumo J., Arimoto S., and Yoshizawa S. An active pulse transmission line simulating nerve axon. Proc. IRE 50 (1962) 2061-2070
    • (1962) Proc. IRE , vol.50 , pp. 2061-2070
    • Nagumo, J.1    Arimoto, S.2    Yoshizawa, S.3
  • 37
    • 0001247610 scopus 로고    scopus 로고
    • Self-synchronization of coupled oscillators with hysteretic responses
    • Tanaka H., Lichtenberg A.J., and Oishi S. Self-synchronization of coupled oscillators with hysteretic responses. Physica D 100 (1997) 279-300
    • (1997) Physica D , vol.100 , pp. 279-300
    • Tanaka, H.1    Lichtenberg, A.J.2    Oishi, S.3
  • 38
    • 0033534270 scopus 로고    scopus 로고
    • Noise effects on synchronization in systems of coupled oscillators
    • Hong H., et al. Noise effects on synchronization in systems of coupled oscillators. J. Phys. A 32 (1999) L9-L15
    • (1999) J. Phys. A , vol.32
    • Hong, H.1
  • 39
    • 0034272217 scopus 로고    scopus 로고
    • Synchronization in populations of globally coupled oscillators with inertial effects
    • Acebrón J.A., Bonilla L.L., and Spigler R. Synchronization in populations of globally coupled oscillators with inertial effects. Phys. Rev. E 62 (2000) 3437-3454
    • (2000) Phys. Rev. E , vol.62 , pp. 3437-3454
    • Acebrón, J.A.1    Bonilla, L.L.2    Spigler, R.3
  • 40
    • 5944222448 scopus 로고
    • An adaptive model for synchrony in the firefly Pteroptyx malaccae
    • Ermentrout G.B. An adaptive model for synchrony in the firefly Pteroptyx malaccae. J. Math. Biol. 29 (1991) 571-585
    • (1991) J. Math. Biol. , vol.29 , pp. 571-585
    • Ermentrout, G.B.1
  • 41
    • 27144505149 scopus 로고    scopus 로고
    • Phase resetting and transient desynchronization in networks of globally coupled phase oscillators with inertia
    • Dolana K., Majtanika M., and Tass P.A. Phase resetting and transient desynchronization in networks of globally coupled phase oscillators with inertia. Physica D 211 (2005) 128-138
    • (2005) Physica D , vol.211 , pp. 128-138
    • Dolana, K.1    Majtanika, M.2    Tass, P.A.3
  • 42
    • 0013010950 scopus 로고    scopus 로고
    • Springer-Verlag, Berlin
    • Haken H. Brain Dynamics (2002), Springer-Verlag, Berlin
    • (2002) Brain Dynamics
    • Haken, H.1
  • 43
    • 0016919435 scopus 로고
    • Mode analysis of a multimode ladder oscillator circuits and systems
    • Endo T., and Mori S. Mode analysis of a multimode ladder oscillator circuits and systems. IEEE Trans. Circuits Syst. 23 (1976) 100-113
    • (1976) IEEE Trans. Circuits Syst. , vol.23 , pp. 100-113
    • Endo, T.1    Mori, S.2
  • 44
    • 0017973934 scopus 로고
    • Multimode oscillations in mutually coupled van der Pol type oscillators with fifth-power nonlinear characteristics
    • Datardina S., and Linkens D. Multimode oscillations in mutually coupled van der Pol type oscillators with fifth-power nonlinear characteristics. IEEE Trans. Circuits Syst. 25 (1978) 308-315
    • (1978) IEEE Trans. Circuits Syst. , vol.25 , pp. 308-315
    • Datardina, S.1    Linkens, D.2
  • 45
    • 0142155104 scopus 로고    scopus 로고
    • Phase-waves in a ladder of oscillators
    • Yamauchi M., Nishio Y., and Ushida A. Phase-waves in a ladder of oscillators. IEICE Trans. E86 (2003) 891-899
    • (2003) IEICE Trans. , vol.E86 , pp. 891-899
    • Yamauchi, M.1    Nishio, Y.2    Ushida, A.3
  • 47
    • 70349496441 scopus 로고    scopus 로고
    • Effects of noise and variations on the duration of transient oscillations in unidirectionally coupled bistable ring networks
    • Horikawa Y., and Kitajima H. Effects of noise and variations on the duration of transient oscillations in unidirectionally coupled bistable ring networks. Phys. Rev. E 80 (2009) 021934/1-021934/15
    • (2009) Phys. Rev. E , vol.80
    • Horikawa, Y.1    Kitajima, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.