메뉴 건너뛰기




Volumn 9, Issue 1, 2008, Pages 9-25

Hopf bifurcation analysis in a tri-neuron network with time delay

Author keywords

Hopf bifurcation; Neural network; Periodic solutions; Time delay

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; NEURAL NETWORKS; THEOREM PROVING; TIME DELAY;

EID: 35248882076     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2006.08.008     Document Type: Article
Times cited : (43)

References (21)
  • 1
    • 0028468031 scopus 로고
    • How delays affect neural dynamics and learning
    • Baldi P., and Atiya A. How delays affect neural dynamics and learning. IEEE Trans. Neural Networks 5 (1994) 610-621
    • (1994) IEEE Trans. Neural Networks , vol.5 , pp. 610-621
    • Baldi, P.1    Atiya, A.2
  • 2
    • 34248352395 scopus 로고
    • Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback
    • Campbell S.A., Belair J., Ohira T., and Milton J. Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback. J. Dynamic Differential Equations 7 1 (1995) 213-236
    • (1995) J. Dynamic Differential Equations , vol.7 , Issue.1 , pp. 213-236
    • Campbell, S.A.1    Belair, J.2    Ohira, T.3    Milton, J.4
  • 3
    • 0001115830 scopus 로고    scopus 로고
    • Minimal instability and unstable set of a phase-locked periodic orbit in a delayed neural network
    • Chen Y., and Wu J. Minimal instability and unstable set of a phase-locked periodic orbit in a delayed neural network. Physica D 134 (1999) 185-199
    • (1999) Physica D , vol.134 , pp. 185-199
    • Chen, Y.1    Wu, J.2
  • 4
    • 0035402689 scopus 로고    scopus 로고
    • Slowly oscillating periodic solutions for a delayed frustrated network for two neurons
    • Chen Y., and Wu J. Slowly oscillating periodic solutions for a delayed frustrated network for two neurons. J. Math. Anal. Appl. 259 (2001) 188-208
    • (2001) J. Math. Anal. Appl. , vol.259 , pp. 188-208
    • Chen, Y.1    Wu, J.2
  • 5
    • 0038346772 scopus 로고    scopus 로고
    • Existence and attraction of a phase-locked oscillation in a delayed frustrated network for two neurons
    • Chen Y., and Wu J. Existence and attraction of a phase-locked oscillation in a delayed frustrated network for two neurons. Differential Integral Equations 14 (2001) 1181-1236
    • (2001) Differential Integral Equations , vol.14 , pp. 1181-1236
    • Chen, Y.1    Wu, J.2
  • 6
    • 0034693565 scopus 로고    scopus 로고
    • On a planar system modelling a neuron network with memory
    • Faria T. On a planar system modelling a neuron network with memory. J. Differential Equations 168 (2000) 129-149
    • (2000) J. Differential Equations , vol.168 , pp. 129-149
    • Faria, T.1
  • 7
    • 0041511877 scopus 로고    scopus 로고
    • Hopf bifurcating periodic orbits in a ring of neurons with delays
    • Guo S., and Huang L. Hopf bifurcating periodic orbits in a ring of neurons with delays. Pyhsica D 183 (2003) 19-44
    • (2003) Pyhsica D , vol.183 , pp. 19-44
    • Guo, S.1    Huang, L.2
  • 11
    • 1842465386 scopus 로고    scopus 로고
    • On the zeros of transcendental functions with applications to stability of delay differential equations with two delays
    • Ruan S., and Wei J. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamics Continuous, Discrete Impulsive Systems Ser. A: Math. Anal. 10 (2003) 863-874
    • (2003) Dynamics Continuous, Discrete Impulsive Systems Ser. A: Math. Anal. , vol.10 , pp. 863-874
    • Ruan, S.1    Wei, J.2
  • 12
    • 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 2 (2000) 673-700
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.2 , pp. 673-700
    • Shayer, L.1    Campbell, S.2
  • 13
    • 12244261643 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation on a simplified BAM neural network with delays
    • Song Y., Han M., and Wei J. Stability and Hopf bifurcation on a simplified BAM neural network with delays. Physica D 200 (2005) 185-204
    • (2005) Physica D , vol.200 , pp. 185-204
    • Song, Y.1    Han, M.2    Wei, J.3
  • 14
    • 2342442918 scopus 로고    scopus 로고
    • Hopf bifurcation in bidirectional associative memory neural networks with delays: analysis and computation
    • Wang L., and Zou X. Hopf bifurcation in bidirectional associative memory neural networks with delays: analysis and computation. J. Comput. Appl. Math. 167 (2004) 73-90
    • (2004) J. Comput. Appl. Math. , vol.167 , pp. 73-90
    • Wang, L.1    Zou, X.2
  • 15
    • 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
  • 16
    • 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
  • 17
    • 7244227815 scopus 로고    scopus 로고
    • Bifurcation analysis and existence of periodic solutions in a simple neural network with delays
    • Wei J., and Velarde M. Bifurcation analysis and existence of periodic solutions in a simple neural network with delays. Chaos 14 3 (2004) 940-952
    • (2004) Chaos , vol.14 , Issue.3 , pp. 940-952
    • Wei, J.1    Velarde, M.2
  • 18
    • 27644482807 scopus 로고    scopus 로고
    • Synchronized Hopf bifurcation analysis in a neural network model with delays
    • Wei J., and Yuan Y. Synchronized Hopf bifurcation analysis in a neural network model with delays. J. Math. Anal. Appl. 312 (2005) 205-229
    • (2005) J. Math. Anal. Appl. , vol.312 , pp. 205-229
    • Wei, J.1    Yuan, Y.2
  • 19
    • 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
  • 20
    • 0033166162 scopus 로고    scopus 로고
    • Synchronization and stable phase-locking in a network of neurons with memory
    • Wu J., Faria T., and Huang Y.S. Synchronization and stable phase-locking in a network of neurons with memory. Math. Comput. Modelling 30 (1999) 117-138
    • (1999) Math. Comput. Modelling , vol.30 , pp. 117-138
    • Wu, J.1    Faria, T.2    Huang, Y.S.3
  • 21
    • 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 2 (2006) 579-595
    • (2006) J. Comput. Appl. Math. , vol.196 , Issue.2 , pp. 579-595
    • Yan, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.