In this paper, based on the theory of fractional-order calculus, we obtain some sufficient conditions for the uniform stability of fractional-order fuzzy BAM neural networks with delays in the leakage terms. Moreover, the existence, uniqueness and stability of its equilibrium point are also proved. A numerical example is presented to demonstrate the validity and feasibility of the proposed results.
Podlubny, I. (1999) Fractional Differential Equations. Academic Press, San Diego.
Kilbas, A.A. (2006) Theory and Application of Fractional Differential Equations. Elsevier, Amsterdam.
Samko, S.G., Kilbas, A.A. and Marichev, Q.I. (1993) Fractional Integrals and Derivatives. Gordon and Breach Science, Yverdon.
Magin, R.L. (2006) Fractional Calculus in Bioengineering. Begell House, Connecticut.
Bastos, N.R.O., Ferreira, R.A.C. and Torres, D.F.M. (2011) Discrete-Time Fractional Variational Problems. Signal Process, 91, 513-524. https://doi.org/10.1016/j.sigpro.2010.05.001
Kaslika, E. and Sivasundaram, S. (2012) Nonlinear Dynamics and Chaos in Fractional Order Neural Networks. Neural Networks, 32, 245-256. https://doi.org/10.1016/j.neunet.2012.02.030
Yang, X.J., Song, Q.K., Liu, Y.R. and Zhao, Z.J. (2015) Finite-Time Stability Analysis of Fractional-Order Neural Networks with Delay. Neurocomputing, 152, 19-26. https://doi.org/10.1016/j.neucom.2014.11.023
Zhang, S., Yu, Y.G. and Wang, Q. (2016) Stability Analysis of Fractional-Order Hopfield Neural Networks with Discontinuous Activation Functions. Neurocomputing, 171, 1075-1084. https://doi.org/10.1016/j.neucom.2015.07.077
Chen, L.P., Chai, Y., Wu, R.C., Ma, T.D. and Zhai, H.Z. (2013) Dynamic Analysis of a Class of Fractional-Order Neural Networks with Delay. Neurocomputing, 111, 190-194. https://doi.org/10.1016/j.neucom.2012.11.034
Wang, L.M., Song, Q.K., Liu, Y.R., Zhao, Z.J. and Alsaadi, F.E. (2017) Global Asymptotic Stability of Impulsive Fractional-Order Complex-Valued Neural Networks with Time Delay. Neurocomputing, 243, 49-59. https://doi.org/10.1016/j.neucom.2017.02.086
Arena, P., Fortuna, L. and Porto, D. (2000) Chaotic Behavior in Noninteger-Order Cellular Neural Networks. Physical Review E, 61, 776-781. https://doi.org/10.1103/PhysRevE.61.776
Wang, Y., Zheng, C.D. and Feng, E. (2013) Stability Analysis of Mixed Recurrent Neural Networks with Time Delay in the Leakage Term under Impulsive Perturbations. Neurocomputing, 119, 454-461. https://doi.org/10.1016/j.neucom.2013.03.012
Li, R.X. and Cao, J.D. (2016) Stability Analysis of Reaction-Diffusion Uncertain Memristive Neural Networks with Time-Varying Delays and Leakage Term. Applied Mathematics and Computation, 278, 54-69. https://doi.org/10.1016/j.amc.2016.01.016
Kalpanaa, M. and Balasubramaniam, P. (2016) Asymptotical State Estimation of Fuzzy Cellular Neural Networks with Time Delay in the Leakage Term and Mixed Delays: Sample-Data Approach. Journal of the Egyptian Mathematical Society, 24, 143-150. https://doi.org/10.1016/j.joems.2014.07.003
Liu, J. and Xu, R. (2017) Delay-Dependent Passivity and Stability Analysis for a Class of Memristor-Based Neural Networks with Time Delay in the Leakage Term. Neural Processing Letters, 46, 467-485. https://doi.org/10.1007/s11063-017-9594-6
Wang, L.M., Song, Q.K., Liu, Y.R., Zhao, Z.J. and Alsaadi, F.E. (2017) Finite-Time Stability Analysis of Fractional-Order Complex-Valued Memristor-Based Neural Networks with Both Leakage and Time-Varying Delays. Neurocomputing, 245, 86-101. https://doi.org/10.1016/j.neucom.2017.03.042
Yang, T., Yang, L.B., Wu, C.W. and Chua, L.O. (1996) Fuzzy Cellular Neural Networks: Theory. 1996 Fourth IEEE International Workshop on Cellular Neural Networks and Their Applications, Seville, 24-26 June 1996, 181-186.
Yang, T., Yang, L.B., Wu, C.W. and Chua, L.O. (1996) Fuzzy Cellular Neural Networks: Applications. 1996 Fourth IEEE International Workshop on Cellular Neural Networks and Their Applications, Seville, 24-26 June 1996, 225-230.
Ali, M.S., Balasubramaniam, P. and Zhu, Q.X. (2017) Stability of Stochastic Fuzzy BAM Neural Networks with Discrete and Distributed Time-Varying Delays. International Journal of Machine Learning and Cybernetics, 8, 263-273. https://doi.org/10.1007/s13042-014-0320-7
Li, Y.K. and Li, Y.Q. (2014) Exponential Stability of BAM Fuzzy Cellular Neural Networks with Time-Varying Delays in Leakage Terms and Impulses. Abstract and Applied Analysis, 2014, 1-12.
He, W.N. and Chu, L.X. (2017) Exponential Stability Criteria for Fuzzy Bidirectional Associative Memory Cohen-Grossberg Neural Networks with Mixed Delays and Impulses. Advances in Difference Equations, 2017, 61. https://doi.org/10.1186/s13662-017-1082-9
Bao, H.M. (2016) Existence and Exponential Stability of Periodic Solution for BAM Fuzzy Cohen-Grossberg Neural Networks with Mixed Delays. Neural Processing Letters, 43, 871-885. https://doi.org/10.1007/s11063-015-9455-0
Delavari, H., Baleanu, D. and Sadati, J. (2012) Stability Analysis of Caputo Fractional Order Nonlinear Systems Revisited. Nonlinear Dynamics, 67, 2433-2439. https://doi.org/10.1007/s11071-011-0157-5
Li, Y., Chen, Y. and Podlubny, I. (2010) Stability of Fractional-Order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag-Leffler Stability. Computers and Mathematics with Applications, 59, 1810-1821. https://doi.org/10.1016/j.camwa.2009.08.019
Yang, T. and Yang, L. (1996) The Global Stability of Fuzzy Cellular Neural Networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 43, 880-883. https://doi.org/10.1109/81.538999