메뉴 건너뛰기




Volumn 23, Issue 2, 2010, Pages 189-200

Coexistence and local stability of multiple equilibria in neural networks with piecewise linear nondecreasing activation functions

Author keywords

Attraction basin; Coexistence; Multiple equilibria; Multistability; Neural networks

Indexed keywords

ACTIVATION FUNCTIONS; ATTRACTION BASIN; CORNER POINT; EXPONENTIALLY STABLE; LOCAL STABILITY; MULTIPLE EQUILIBRIA; MULTIPLE EQUILIBRIUM; MULTISTABILITY; PIECEWISE LINEAR; PIECEWISE LINEAR ACTIVATIONS; STABLE EQUILIBRIUM POINTS; STABLE MANIFOLD; UNSTABLE EQUILIBRIUM POINTS;

EID: 73949135312     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2009.11.010     Document Type: Article
Times cited : (105)

References (19)
  • 1
    • 45049087176 scopus 로고    scopus 로고
    • Multistability and multiperiodicity of delayed Cohen-Grossberg neural networks with a general class of activation functions
    • Cao J., Feng G., and Wang Y. Multistability and multiperiodicity of delayed Cohen-Grossberg neural networks with a general class of activation functions. Physica D: Nonlinear Phenomena 237 13 (2008) 1734-1749
    • (2008) Physica D: Nonlinear Phenomena , vol.237 , Issue.13 , pp. 1734-1749
    • Cao, J.1    Feng, G.2    Wang, Y.3
  • 2
    • 0034849714 scopus 로고    scopus 로고
    • Global exponential stability of delayed hopfield neural networks
    • Chen T. Global exponential stability of delayed hopfield neural networks. Neural Networks 14 8 (2001) 977-980
    • (2001) Neural Networks , vol.14 , Issue.8 , pp. 977-980
    • Chen, T.1
  • 3
    • 0035312613 scopus 로고    scopus 로고
    • New theorems on global convergence of some dynamical systems
    • Chen T., and Amari S. New theorems on global convergence of some dynamical systems. Neural Networks 14 (2001) 251-255
    • (2001) Neural Networks , vol.14 , pp. 251-255
    • Chen, T.1    Amari, S.2
  • 4
    • 33845215509 scopus 로고    scopus 로고
    • Multistability and convergence in delayed neural networks
    • Cheng C., Lin K., and Shih C. Multistability and convergence in delayed neural networks. Physica D: Nonlinear Phenomena 225 1 (2007) 61-74
    • (2007) Physica D: Nonlinear Phenomena , vol.225 , Issue.1 , pp. 61-74
    • Cheng, C.1    Lin, K.2    Shih, C.3
  • 6
    • 0020970741 scopus 로고
    • Absolute stability of global pattern formation and parallel memory storage by competitive neural networks
    • Cohen M.A., and Grossberg S. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man and Cybernetics 13 5 (1983) 815-826
    • (1983) IEEE Transactions on Systems, Man and Cybernetics , vol.13 , Issue.5 , pp. 815-826
    • Cohen, M.A.1    Grossberg, S.2
  • 8
    • 0016737517 scopus 로고
    • Pattern formation, contrast control, and oscillations in the short term memory of shunting on-center off-surround networks
    • Ellias S.A., and Grossberg S. Pattern formation, contrast control, and oscillations in the short term memory of shunting on-center off-surround networks. Biological Cybernetics 20 (1975) 69-98
    • (1975) Biological Cybernetics , vol.20 , pp. 69-98
    • Ellias, S.A.1    Grossberg, S.2
  • 9
    • 84961365499 scopus 로고
    • Contour enhancement, short term memory, and constancies in reverberating neural networks
    • Grossberg S. Contour enhancement, short term memory, and constancies in reverberating neural networks. Studies in Applied Mathematics (1973) 213-257
    • (1973) Studies in Applied Mathematics , pp. 213-257
    • Grossberg, S.1
  • 10
    • 0034702306 scopus 로고    scopus 로고
    • Digital selection and analogue amplification coexist in a cortex inspired silicon circuit
    • Hahnloser R., Sarpeshkar R., Mahowald M., Douglas R., and Seung H. Digital selection and analogue amplification coexist in a cortex inspired silicon circuit. Nature 405 (2000) 947-951
    • (2000) Nature , vol.405 , pp. 947-951
    • Hahnloser, R.1    Sarpeshkar, R.2    Mahowald, M.3    Douglas, R.4    Seung, H.5
  • 11
    • 34548049546 scopus 로고    scopus 로고
    • Multistability in spiking neuron models of delayed recurrent inhibitory loops
    • Ma J., and Wu J. Multistability in spiking neuron models of delayed recurrent inhibitory loops. Neural Computation 19 (2007) 2124-2148
    • (2007) Neural Computation , vol.19 , pp. 2124-2148
    • Ma, J.1    Wu, J.2
  • 12
    • 49549085003 scopus 로고    scopus 로고
    • Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework
    • Remy É., Ruet P., and Thieffry D. Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework. Advances in Applied Mathematics 41 (2008) 335-350
    • (2008) Advances in Applied Mathematics , vol.41 , pp. 335-350
    • Remy, É.1    Ruet, P.2    Thieffry, D.3
  • 13
    • 0342936163 scopus 로고    scopus 로고
    • Stability, bifurcation, and multistability in a system of two coupled neurons with multiple time delays
    • Shayer L.P., and Campbell S.A. Stability, bifurcation, and multistability in a system of two coupled neurons with multiple time delays. SIAM Journal on Applied Mathematics 61 2 (2000) 673-700
    • (2000) SIAM Journal on Applied Mathematics , vol.61 , Issue.2 , pp. 673-700
    • Shayer, L.P.1    Campbell, S.A.2
  • 14
    • 0035432452 scopus 로고    scopus 로고
    • Dynamical stability conditions for recurrent neural networks with unsaturating piecewise linear transfer functions
    • Wersing H., Beyn W.J., and Ritter H. Dynamical stability conditions for recurrent neural networks with unsaturating piecewise linear transfer functions. Neural Computation 13 8 (2001) 1811-1825
    • (2001) Neural Computation , vol.13 , Issue.8 , pp. 1811-1825
    • Wersing, H.1    Beyn, W.J.2    Ritter, H.3
  • 15
    • 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. Biophysical Journal 12 (1972) 1-24
    • (1972) Biophysical Journal , vol.12 , pp. 1-24
    • Wilson, H.R.1    Cowan, J.D.2
  • 16
    • 0015868589 scopus 로고
    • A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
    • Wilson H.R., and Cowan J.D. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Biological Cybernetics (1973) 55-80
    • (1973) Biological Cybernetics , pp. 55-80
    • Wilson, H.R.1    Cowan, J.D.2
  • 17
    • 33645704613 scopus 로고    scopus 로고
    • Multiperiodicity and exponential attractivity evoked by periodic external inputs in delayed cellular neural networks
    • Zeng Z., and Wang J. Multiperiodicity and exponential attractivity evoked by periodic external inputs in delayed cellular neural networks. Neural Computation 18 (2006) 848-870
    • (2006) Neural Computation , vol.18 , pp. 848-870
    • Zeng, Z.1    Wang, J.2
  • 18
    • 2442432590 scopus 로고    scopus 로고
    • Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions
    • Zhang Y., and Tan K. Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions. IEEE Transactions on Neural Networks 15 2 (2004) 329-336
    • (2004) IEEE Transactions on Neural Networks , vol.15 , Issue.2 , pp. 329-336
    • Zhang, Y.1    Tan, K.2
  • 19
    • 39549123043 scopus 로고    scopus 로고
    • Multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions
    • Zhang L., Yi Z., and Yu J. Multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions. IEEE Transactions on Neural Networks 19 1 (2008) 158-167
    • (2008) IEEE Transactions on Neural Networks , vol.19 , Issue.1 , pp. 158-167
    • Zhang, L.1    Yi, Z.2    Yu, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.