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Volumn 26, Issue 1, 2015, Pages 84-97

Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays

Author keywords

Banach contraction fixed point theorem; complex valued neural networks; fractional order; time delays.

Indexed keywords

COMPLEX NETWORKS; FIXED POINT ARITHMETIC; TIME DELAY;

EID: 84919636037     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2014.2311099     Document Type: Article
Times cited : (263)

References (40)
  • 2
    • 36348976811 scopus 로고    scopus 로고
    • Fractional calculus: A mathematical tool from the past for present engineers
    • Apr.
    • D. Cafagna, "Fractional calculus: A mathematical tool from the past for present engineers," IEEE Ind. Electron. Mag., vol. 1, no. 2, pp. 35-40, Apr. 2007.
    • (2007) IEEE Ind. Electron. Mag. , vol.1 , Issue.2 , pp. 35-40
    • Cafagna, D.1
  • 5
    • 0010178279 scopus 로고
    • An analog simulation of noninteger order transfer functions for analysis of electrode process
    • Dec.
    • M. Ichise, Y. Nagayanagi, and T. Kojima, "An analog simulation of noninteger order transfer functions for analysis of electrode process," J. Electroanal. Chem. Inter. Electrochem., vol. 33, no. 2, pp. 253-265, Dec. 1971.
    • (1971) J. Electroanal. Chem. Inter. Electrochem. , vol.33 , Issue.2 , pp. 253-265
    • Ichise, M.1    Nagayanagi, Y.2    Kojima, T.3
  • 6
    • 0021424253 scopus 로고
    • Linear approximation of transfer function with a pole of fractional order
    • May
    • H. H. Sun, A. A. Abdelwahad, and B. Onaral, "Linear approximation of transfer function with a pole of fractional order," IEEE Trans. Autom. Control, vol. 29, no. 5, pp. 441-444, May 1984.
    • (1984) IEEE Trans. Autom. Control , vol.29 , Issue.5 , pp. 441-444
    • Sun, H.H.1    Abdelwahad, A.A.2    Onaral, B.3
  • 7
    • 0021440218 scopus 로고
    • Application of fractional calculus to the theory of viscoelasticity
    • Jun.
    • R. C. Koeller, "Application of fractional calculus to the theory of viscoelasticity," J. Appl. Mech., vol. 51, no. 2, pp. 299-307, Jun. 1984.
    • (1984) J. Appl. Mech. , vol.51 , Issue.2 , pp. 299-307
    • Koeller, R.C.1
  • 8
    • 77953685231 scopus 로고    scopus 로고
    • The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems
    • Sep.
    • X. Y. Jiang and M. Y. Xu, "The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems," Phys. A, vol. 389, no. 17, pp. 3368-3374, Sep. 2010.
    • (2010) Phys. A , vol.389 , Issue.17 , pp. 3368-3374
    • Jiang, X.Y.1    Xu, M.Y.2
  • 9
    • 84865615179 scopus 로고    scopus 로고
    • Stability and synchronization for fractional-order neural networks
    • Nov.
    • J. Yu, C. Hu, and H. Jiang, " stability and synchronization for fractional-order neural networks," Neural Netw., vol. 35, pp. 82-87, Nov. 2012.
    • (2012) Neural Netw. , vol.35 , pp. 82-87
    • Yu, J.1    Hu, C.2    Jiang, H.3
  • 10
    • 41849090145 scopus 로고    scopus 로고
    • Chaos on the fractional order unified system and its synchronization
    • Jul.
    • X. J. Wu, J. Li, and G. R. Chen, "Chaos on the fractional order unified system and its synchronization," J. Franklin Inst., vol. 345, no. 4, pp. 392-401, Jul. 2008.
    • (2008) J. Franklin Inst. , vol.345 , Issue.4 , pp. 392-401
    • Wu, X.J.1    Li, J.2    Chen, G.R.3
  • 11
    • 18844427587 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional Lu system
    • Aug.
    • W. H. Deng and C. P. Li, "Chaos synchronization of the fractional Lu system," Phys. A, vol. 353, pp. 61-72, Aug. 2005.
    • (2005) Phys. A , vol.353 , pp. 61-72
    • Deng, W.H.1    Li, C.P.2
  • 12
    • 84858841611 scopus 로고    scopus 로고
    • Stability analysis of Caputo fractional-order nonlinear systems revisited
    • Mar.
    • H. Delavari, D. Baleanu, and J. Sadati, "Stability analysis of Caputo fractional-order nonlinear systems revisited," Nonlinear Dyn., vol. 67, no. 4, pp. 2433-2439, Mar. 2012.
    • (2012) Nonlinear Dyn. , vol.67 , Issue.4 , pp. 2433-2439
    • Delavari, H.1    Baleanu, D.2    Sadati, J.3
  • 13
    • 41649105825 scopus 로고    scopus 로고
    • Generalized projective synchronization of fractional order chaotic systems
    • Jun.
    • G. J. Peng, Y. L. Jiang, and F. Chen, "Generalized projective synchronization of fractional order chaotic systems," Phys. A, vol. 387, no. 14, pp. 3738-3746, Jun. 2008.
    • (2008) Phys. A , vol.387 , Issue.14 , pp. 3738-3746
    • Peng, G.J.1    Jiang, Y.L.2    Chen, F.3
  • 14
    • 65749088733 scopus 로고    scopus 로고
    • Synchronization of a new fractional-order hyperchaotic system
    • Jun.
    • X. J. Wu, H. T. Lu, and S. L. Shen, "Synchronization of a new fractional-order hyperchaotic system," Phys. Lett. A, vol. 373, nos. 27-28, pp. 2329-2337, Jun. 2009.
    • (2009) Phys. Lett. A , vol.373 , Issue.27-28 , pp. 2329-2337
    • Wu, X.J.1    Lu, H.T.2    Shen, S.L.3
  • 15
    • 84885626010 scopus 로고    scopus 로고
    • Learning as a nonlinear line of attraction in a recurrent neural network
    • Mar.
    • M. J. Seow, V. K. Asari, and A. Livingston, "Learning as a nonlinear line of attraction in a recurrent neural network," Neural Comput. Appl., vol. 19, no. 2, pp. 337-342, Mar. 2010.
    • (2010) Neural Comput. Appl. , vol.19 , Issue.2 , pp. 337-342
    • Seow, M.J.1    Asari, V.K.2    Livingston, A.3
  • 16
    • 84919644043 scopus 로고    scopus 로고
    • Performance evaluation of complex valued neural networks using various error functions
    • A. S. Gangal, P. K. Kalra, and D. S. Chauhan, "Performance evaluation of complex valued neural networks using various error functions," Int. J. Electr. Electron. Sci. Eng., vol. 1, no. 5, pp. 41-46, 2007.
    • (2007) Int. J. Electr. Electron. Sci. Eng. , vol.1 , Issue.5 , pp. 41-46
    • Gangal, A.S.1    Kalra, P.K.2    Chauhan, D.S.3
  • 17
    • 80455154999 scopus 로고    scopus 로고
    • Multistability of second-order competitive neural networks with nondecreasing saturated activation functions
    • Nov.
    • X. Nie and J. Cao, "Multistability of second-order competitive neural networks with nondecreasing saturated activation functions," IEEE Trans. Neural Netw., vol. 22, no. 11, pp. 1694-1708, Nov. 2011.
    • (2011) IEEE Trans. Neural Netw. , vol.22 , Issue.11 , pp. 1694-1708
    • Nie, X.1    Cao, J.2
  • 18
    • 34047142309 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation in a simplified BAM neural network with two time delays
    • Mar.
    • J. Cao and M. Xiao, "Stability and Hopf bifurcation in a simplified BAM neural network with two time delays," IEEE Trans. Neural Netw., vol. 18, no. 2, pp. 416-430, Mar. 2007.
    • (2007) IEEE Trans. Neural Netw. , vol.18 , Issue.2 , pp. 416-430
    • Cao, J.1    Xiao, M.2
  • 19
    • 44349110244 scopus 로고    scopus 로고
    • Global asymptotic stability of recurrent neural networks with multiple time-varying delays
    • May
    • H. Zhang, Z. Wang, and D. Liu, "Global asymptotic stability of recurrent neural networks with multiple time-varying delays," IEEE Trans. Neural Netw., vol. 19, no. 5, pp. 855-873, May 2008.
    • (2008) IEEE Trans. Neural Netw. , vol.19 , Issue.5 , pp. 855-873
    • Zhang, H.1    Wang, Z.2    Liu, D.3
  • 20
    • 44349132890 scopus 로고    scopus 로고
    • Stability and Hopf bifurcation of a general delayed recurrent neural network
    • May
    • W. Yu, J. Cao, and G. Chen, "Stability and Hopf bifurcation of a general delayed recurrent neural network," IEEE Trans. Neural Netw., vol. 19, no. 5, pp. 845-854, May 2008.
    • (2008) IEEE Trans. Neural Netw. , vol.19 , Issue.5 , pp. 845-854
    • Yu, W.1    Cao, J.2    Chen, G.3
  • 21
    • 84865321328 scopus 로고    scopus 로고
    • Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays
    • Mar.
    • Q. Zhu and J. Cao, "Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 3, pp. 467-479, Mar. 2012.
    • (2012) IEEE Trans. Neural Netw. Learn. Syst. , vol.23 , Issue.3 , pp. 467-479
    • Zhu, Q.1    Cao, J.2
  • 22
    • 84984772459 scopus 로고    scopus 로고
    • Fractional differentiation by neocortical pyramidal neurons
    • Nov.
    • B. Lundstrom, M. Higgs, W. Spain, and A. Fairhall, "Fractional differentiation by neocortical pyramidal neurons," Nature Neurosci., vol. 11, no. 11, pp. 1335-1342, Nov. 2008.
    • (2008) Nature Neurosci. , vol.11 , Issue.11 , pp. 1335-1342
    • Lundstrom, B.1    Higgs, M.2    Spain, W.3    Fairhall, A.4
  • 23
    • 84865656162 scopus 로고    scopus 로고
    • Fractional neural network approximation
    • Sep.
    • G. Anastassiou, "Fractional neural network approximation," Comput. Math. Appl., vol. 64, no. 6, pp. 1655-1676, Sep. 2012.
    • (2012) Comput. Math. Appl. , vol.64 , Issue.6 , pp. 1655-1676
    • Anastassiou, G.1
  • 24
    • 84876741903 scopus 로고    scopus 로고
    • Dynamic analysis of a class of fractional-order neural networks with delay
    • Jul.
    • L. Chen, Y. Chai, R. Wu, T. Ma, and H. Zhai, "Dynamic analysis of a class of fractional-order neural networks with delay," Neurocomputing, vol. 111, pp. 190-194, Jul. 2013.
    • Neurocomputing , vol.111 , Issue.2013 , pp. 190-194
    • Chen, L.1    Chai, Y.2    Wu, R.3    Ma, T.4    Zhai, H.5
  • 25
    • 84861764006 scopus 로고    scopus 로고
    • Nonlinear dynamics and chaos in fractional-order neural networks
    • Aug.
    • E. Kaslik and S. Sivasundaram, "Nonlinear dynamics and chaos in fractional-order neural networks," Neural Netw., vol. 32, pp. 245-256, Aug. 2012.
    • (2012) Neural Netw. , vol.32 , pp. 245-256
    • Kaslik, E.1    Sivasundaram, S.2
  • 26
    • 1442346520 scopus 로고    scopus 로고
    • Chaotic behavior in noninteger order cellular neural networks
    • Jan.
    • P. Arena, L. Fortuna, and D. Porto, "Chaotic behavior in noninteger order cellular neural networks," Phys. Rev. E, vol. 61, no. 1, pp. 776-781, Jan. 2000.
    • (2000) Phys. Rev. e , vol.61 , Issue.1 , pp. 776-781
    • Arena, P.1    Fortuna, L.2    Porto, D.3
  • 27
    • 38349181868 scopus 로고    scopus 로고
    • Chaos control and synchronization in a fractional neuron network system
    • May
    • S. Zhou, H. Li, and Z. Zhu, "Chaos control and synchronization in a fractional neuron network system," Chaos, Solitons Fractals, vol. 36, no. 4, pp. 973-984, May 2008.
    • (2008) Chaos, Solitons Fractals , vol.36 , Issue.4 , pp. 973-984
    • Zhou, S.1    Li, H.2    Zhu, Z.3
  • 28
    • 84875905150 scopus 로고    scopus 로고
    • Global stability of complex-valued recurrent neural networks with time-delays
    • Jun.
    • J. Hu and J. Wang, "Global stability of complex-valued recurrent neural networks with time-delays," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 6, pp. 853-865, Jun. 2012.
    • (2012) IEEE Trans. Neural Netw. Learn. Syst. , vol.23 , Issue.6 , pp. 853-865
    • Hu, J.1    Wang, J.2
  • 31
    • 84859707632 scopus 로고    scopus 로고
    • Global stability of complexvalued neural networks on time scales
    • Jan.
    • M. Bohner, V. S. H. Rao, and S. Sanyal, "Global stability of complexvalued neural networks on time scales," Differ. Equ. Dyn. Syst., vol. 19, nos. 1-2, pp. 3-11, Jan. 2011.
    • (2011) Differ. Equ. Dyn. Syst. , vol.19 , Issue.1-2 , pp. 3-11
    • Bohner, M.1    Rao, V.S.H.2    Sanyal, S.3
  • 32
    • 0035440681 scopus 로고    scopus 로고
    • Relaxation of the stability condition of the complexvalued neural networks
    • Sep.
    • D. L. Lee, "Relaxation of the stability condition of the complexvalued neural networks," IEEE Trans. Neural Netw., vol. 12, no. 5, pp. 1260-1262, Sep. 2001.
    • (2001) IEEE Trans. Neural Netw. , vol.12 , Issue.5 , pp. 1260-1262
    • Lee, D.L.1
  • 33
    • 79952314531 scopus 로고    scopus 로고
    • Nature of complex number and complex-valued neural networks
    • Mar.
    • A. Hirose, "Nature of complex number and complex-valued neural networks," Frontiers Electr. Electron. Eng. China, vol. 6, no. 1, pp. 171-180, Mar. 2011.
    • (2011) Frontiers Electr. Electron. Eng. China , vol.6 , Issue.1 , pp. 171-180
    • Hirose, A.1
  • 34
    • 79960276196 scopus 로고    scopus 로고
    • Complex valued neural network with Mobius activation function
    • Dec.
    • N. Ozdemir, B. B. Iskender, and N. Y. Ozgur, "Complex valued neural network with Mobius activation function," Commun. Nonlinear Sci. Numer. Simul., vol. 16, no. 12, pp. 4698-4703, Dec. 2011.
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.16 , Issue.12 , pp. 4698-4703
    • Ozdemir, N.1    Iskender, B.B.2    Ozgur, N.Y.3
  • 35
    • 79959214615 scopus 로고    scopus 로고
    • Complex-valued Zhang neural network for online complex-valued time-varying matrix inversion
    • Aug.
    • Y. Zhang, Z. Li, and K. Li, "Complex-valued Zhang neural network for online complex-valued time-varying matrix inversion," Appl. Math. Comput., vol. 217, no. 24, pp. 10066-10073, Aug. 2011.
    • (2011) Appl. Math. Comput. , vol.217 , Issue.24 , pp. 10066-10073
    • Zhang, Y.1    Li, Z.2    Li, K.3
  • 37
  • 38
    • 34247212711 scopus 로고    scopus 로고
    • Remarks on fractional derivatives
    • Apr.
    • C. P. Li and W. H. Deng, "Remarks on fractional derivatives," Appl. Math. Comput., vol. 187, no. 2, pp. 777-784, Apr. 2007.
    • (2007) Appl. Math. Comput. , vol.187 , Issue.2 , pp. 777-784
    • Li, C.P.1    Deng, W.H.2
  • 39
    • 0001618393 scopus 로고    scopus 로고
    • An algorithm for the numerical solution of differential equations of fractional order
    • K. Diethelm, "An algorithm for the numerical solution of differential equations of fractional order," Electron. Trans. Numer. Anal., vol. 5, no. 1, pp. 1-6, 1997.
    • (1997) Electron. Trans. Numer. Anal. , vol.5 , Issue.1 , pp. 1-6
    • Diethelm, K.1
  • 40
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • Jul.
    • K. Diethelm, N. J. Ford, and A. D. Freed, "A predictor-corrector approach for the numerical solution of fractional differential equations," Nonlinear Dyn., vol. 29, nos. 1-4, pp. 3-22, Jul. 2002.
    • (2002) Nonlinear Dyn. , vol.29 , Issue.1-4 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3


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