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Volumn 32, Issue , 2012, Pages 245-256

Nonlinear dynamics and chaos in fractional-order neural networks

Author keywords

Chaos; Fractance; Fractional order; Hopf bifurcation; Hub; Multistability; Neural networks; Ring; Stability; Strange attractor

Indexed keywords

FRACTANCE; FRACTIONAL ORDER; HUB; MULTISTABILITY; STRANGE ATTRACTORS;

EID: 84861764006     PISSN: 08936080     EISSN: 18792782     Source Type: Journal    
DOI: 10.1016/j.neunet.2012.02.030     Document Type: Article
Times cited : (392)

References (50)
  • 1
    • 64249092279 scopus 로고    scopus 로고
    • Some existence results for fractional integro-differential equations with nonlinear conditions
    • Ahmad B., Sivasundaram S. Some existence results for fractional integro-differential equations with nonlinear conditions. Communications in Applied Analysis 2008, 12:107-112.
    • (2008) Communications in Applied Analysis , vol.12 , pp. 107-112
    • Ahmad, B.1    Sivasundaram, S.2
  • 2
    • 70350572941 scopus 로고    scopus 로고
    • Existence of solutions for impulsive integral boundary value problems of fractional order
    • Ahmad B., Sivasundaram S. Existence of solutions for impulsive integral boundary value problems of fractional order. Nonlinear Analysis: Hybrid Systems 2010, 4:134-141.
    • (2010) Nonlinear Analysis: Hybrid Systems , vol.4 , pp. 134-141
    • Ahmad, B.1    Sivasundaram, S.2
  • 3
    • 0028696254 scopus 로고
    • The fractional-order dynamics of brainstem vestibulo-oculomotor neurons
    • Anastasio T. The fractional-order dynamics of brainstem vestibulo-oculomotor neurons. Biological Cybernetics 1994, 72:69-79.
    • (1994) Biological Cybernetics , vol.72 , pp. 69-79
    • Anastasio, T.1
  • 4
    • 1442346520 scopus 로고    scopus 로고
    • Chaotic behavior in noninteger-order cellular neural networks
    • Arena P., Fortuna L., Porto D. Chaotic behavior in noninteger-order cellular neural networks. Physical Review E 2000, 61:776-781.
    • (2000) Physical Review E , vol.61 , pp. 776-781
    • Arena, P.1    Fortuna, L.2    Porto, D.3
  • 7
    • 0038483826 scopus 로고    scopus 로고
    • Emergence of scaling in random networks
    • Barabási A.-L., Albert R. Emergence of scaling in random networks. Science 1999, 286:509-512.
    • (1999) Science , vol.286 , pp. 509-512
    • Barabási, A.-L.1    Albert, R.2
  • 8
    • 58249118048 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions to impulsive fractional differential equations
    • Benchohra M., Slimani B. Existence and uniqueness of solutions to impulsive fractional differential equations. Electronic Journal of Differential Equations 2009, 1-11.
    • (2009) Electronic Journal of Differential Equations , pp. 1-11
    • Benchohra, M.1    Slimani, B.2
  • 9
    • 70349105095 scopus 로고    scopus 로고
    • Fractional-order hopfield neural networks
    • Lecture notes in computer science
    • Boroomand A., Menhaj M. Fractional-order hopfield neural networks. LNCS 2009, Vol. 5506:883-890.
    • (2009) LNCS , vol.5506 , pp. 883-890
    • Boroomand, A.1    Menhaj, M.2
  • 10
  • 12
    • 77955267715 scopus 로고    scopus 로고
    • A novel exact representation of stationary colored Gaussian processes (fractional differential approach)
    • Cottone G., Paola M.D., Santoro R. A novel exact representation of stationary colored Gaussian processes (fractional differential approach). Journal of Physics A: Mathematical and Theoretical 2010, 43:085002.
    • (2010) Journal of Physics A: Mathematical and Theoretical , vol.43 , pp. 085002
    • Cottone, G.1    Paola, M.D.2    Santoro, R.3
  • 13
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • Diethelm K., Ford N., Freed A. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics 2002, 29:3-22.
    • (2002) Nonlinear Dynamics , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.2    Freed, A.3
  • 14
    • 61449235428 scopus 로고    scopus 로고
    • On stability, persistence, and hopf bifurcation in fractional order dynamical systems
    • El-Saka H., Ahmed E., Shehata M., El-Sayed A. On stability, persistence, and hopf bifurcation in fractional order dynamical systems. Nonlinear Dynamics 2009, 56:121-126.
    • (2009) Nonlinear Dynamics , vol.56 , pp. 121-126
    • El-Saka, H.1    Ahmed, E.2    Shehata, M.3    El-Sayed, A.4
  • 15
    • 78649591986 scopus 로고    scopus 로고
    • Fractional-order circuits and systems: an emerging interdisciplinary research area
    • Elwakil A. Fractional-order circuits and systems: an emerging interdisciplinary research area. IEEE Circuits and Systems Magazine 2010, 10:40-50.
    • (2010) IEEE Circuits and Systems Magazine , vol.10 , pp. 40-50
    • Elwakil, A.1
  • 16
    • 0031199781 scopus 로고    scopus 로고
    • On the role of fractional calculus in electromagnetic theory
    • Engheia N. On the role of fractional calculus in electromagnetic theory. IEEE Antennas and Propagation Magazine 1997, 39:35-46.
    • (1997) IEEE Antennas and Propagation Magazine , vol.39 , pp. 35-46
    • Engheia, N.1
  • 18
    • 23444456002 scopus 로고    scopus 로고
    • Spatio-temporal patterns of nonlinear oscillations in an excitatory ring network with delay
    • Guo S. Spatio-temporal patterns of nonlinear oscillations in an excitatory ring network with delay. Nonlinearity 2005, 18:2391-2407.
    • (2005) Nonlinearity , vol.18 , pp. 2391-2407
    • Guo, S.1
  • 19
    • 0041511877 scopus 로고    scopus 로고
    • Hopf bifurcating periodic orbits in a ring of neurons with delays
    • Guo S., Huang L. Hopf bifurcating periodic orbits in a ring of neurons with delays. Physica D: Nonlinear Phenomena 2003, 183:19-44.
    • (2003) Physica D: Nonlinear Phenomena , vol.183 , pp. 19-44
    • Guo, S.1    Huang, L.2
  • 21
    • 34247102248 scopus 로고    scopus 로고
    • Stability of nonlinear waves in a ring of neurons with delays
    • Guo S., Huang L. Stability of nonlinear waves in a ring of neurons with delays. Journal of Differential Equations 2007, 236:343-374.
    • (2007) Journal of Differential Equations , vol.236 , pp. 343-374
    • Guo, S.1    Huang, L.2
  • 22
    • 34247111800 scopus 로고    scopus 로고
    • Pattern formation and continuation in a trineuron ring with delays
    • Guo S.J., Huang L.H. Pattern formation and continuation in a trineuron ring with delays. Acta Mathematica Sinica, English Series 2007, 23:799-818.
    • (2007) Acta Mathematica Sinica, English Series , vol.23 , pp. 799-818
    • Guo, S.J.1    Huang, L.H.2
  • 23
    • 0036306866 scopus 로고    scopus 로고
    • Existence of turing instabilities in a two-species fractional reaction-diffusion system
    • Henry B., Wearne S. Existence of turing instabilities in a two-species fractional reaction-diffusion system. SIAM Journal on Applied Mathematics 2002, 62:870-887.
    • (2002) SIAM Journal on Applied Mathematics , vol.62 , pp. 870-887
    • Henry, B.1    Wearne, S.2
  • 24
    • 0001488637 scopus 로고
    • Fractal rheological models and fractional differential equations for viscoelastic behavior
    • Heymans N., Bauwens J.-C. Fractal rheological models and fractional differential equations for viscoelastic behavior. Rheologica Acta 1994, 33:210-219.
    • (1994) Rheologica Acta , vol.33 , pp. 210-219
    • Heymans, N.1    Bauwens, J.-C.2
  • 25
    • 0024909476 scopus 로고
    • Convergent activation dynamics in continuous-time networks
    • Hirsch M. Convergent activation dynamics in continuous-time networks. Neural Networks 1989, 2:331-349.
    • (1989) Neural Networks , vol.2 , pp. 331-349
    • Hirsch, M.1
  • 26
    • 0020118274 scopus 로고
    • Neural networks and physical systems with emergent collective computational abilities
    • Hopfield J. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences 1982, 79:2554-2558.
    • (1982) Proceedings of the National Academy of Sciences , vol.79 , pp. 2554-2558
    • Hopfield, J.1
  • 27
    • 0010178279 scopus 로고
    • An analog simulation of non-integer order transfer functions for analysis of electrode processes
    • Ichise M., Nagayanagi Y., Kojima T. An analog simulation of non-integer order transfer functions for analysis of electrode processes. Journal of Electroanalytical Chemistry 1971, 33:253-265.
    • (1971) Journal of Electroanalytical Chemistry , vol.33 , pp. 253-265
    • Ichise, M.1    Nagayanagi, Y.2    Kojima, T.3
  • 29
    • 71749106122 scopus 로고    scopus 로고
    • Complex and chaotic dynamics in a discrete-time-delayed hopfield neural network with ring architecture
    • Kaslik E., Balint S. Complex and chaotic dynamics in a discrete-time-delayed hopfield neural network with ring architecture. Neural Networks 2009, 22:1411-1418.
    • (2009) Neural Networks , vol.22 , pp. 1411-1418
    • Kaslik, E.1    Balint, S.2
  • 35
    • 45149126186 scopus 로고    scopus 로고
    • Complete classification and stability of equilibria in a delayed ring network
    • Lu X., Guo S. Complete classification and stability of equilibria in a delayed ring network. Electronic Journal of Differential Equations 2008, 2008:1-12.
    • (2008) Electronic Journal of Differential Equations , vol.2008 , pp. 1-12
    • Lu, X.1    Guo, S.2
  • 36
    • 84984772459 scopus 로고    scopus 로고
    • Fractional differentiation by neocortical pyramidal neurons
    • Lundstrom B., Higgs M., Spain W., Fairhall A. Fractional differentiation by neocortical pyramidal neurons. Nature Neuroscience 2008, 11:1335-1342.
    • (2008) Nature Neuroscience , vol.11 , pp. 1335-1342
    • Lundstrom, B.1    Higgs, M.2    Spain, W.3    Fairhall, A.4
  • 37
    • 0030464353 scopus 로고    scopus 로고
    • Fractional relaxation-oscillation and fractional phenomena
    • Mainardi F. Fractional relaxation-oscillation and fractional phenomena. Chaos, Solitons & Fractals 1996, 7:1461-1477.
    • (1996) Chaos, Solitons & Fractals , vol.7 , pp. 1461-1477
    • Mainardi, F.1
  • 38
    • 0002731965 scopus 로고    scopus 로고
    • Stability results for fractional differential equations with applications to control processing
    • Matignon, D. (1996). Stability results for fractional differential equations with applications to control processing. In Computational engineering in systems applications (pp. 963-968).
    • (1996) In Computational engineering in systems applications , pp. 963-968
    • Matignon, D.1
  • 40
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: a fractional dynamics approach
    • Metzler R., Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Physics Reports 2000, 339:1-77.
    • (2000) Physics Reports , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 43
    • 84861769057 scopus 로고    scopus 로고
    • NanoDotTek. What is fractance and why is it useful? Technical report. NDT24-11-2007.
    • NanoDotTek (2007). What is fractance and why is it useful? Technical report. NDT24-11-2007.
    • (2007)
  • 46
    • 0026135818 scopus 로고
    • Burgers equation with a fractional derivative: hereditary effects on nonlinear acoustic waves
    • Sugimoto N. Burgers equation with a fractional derivative: hereditary effects on nonlinear acoustic waves. Journal of Fluid Mechanics 1991, 225:631-653.
    • (1991) Journal of Fluid Mechanics , vol.225 , pp. 631-653
    • Sugimoto, N.1
  • 48
    • 72749127606 scopus 로고    scopus 로고
    • Chaotic synchronization of a fractional neuron network system with time-varying delays
    • In 2009 international conference on communications, circuits and systems. ICCCAS 2009
    • Zhou, S., Hu, P., & Li, H. (2009). Chaotic synchronization of a fractional neuron network system with time-varying delays. In 2009 international conference on communications, circuits and systems. ICCCAS 2009 (pp. 863-867).
    • (2009) , pp. 863-867
    • Zhou, S.1    Hu, P.2    Li, H.3
  • 49
    • 38349181868 scopus 로고    scopus 로고
    • Chaos control and synchronization in a fractional neuron network system
    • Zhou S., Li H., Zhu Z. Chaos control and synchronization in a fractional neuron network system. Chaos, Solitons and Fractals 2008, 36:973-984.
    • (2008) Chaos, Solitons and Fractals , vol.36 , pp. 973-984
    • Zhou, S.1    Li, H.2    Zhu, Z.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.