Abstract
In is paper, we study the problems of stability of the equlibrium with respect to the manifold defined by a function for impulsive fractional-order Cohen-Grossberg neural networks. The effects of variable impulsive perturbations are investigated. The impulses are realized as continuous functions and can be considered as a control. The main results are obtained by employing the Lyapunov method and comparison principle.
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References
Cohen, M.A., Grossberg, S.: Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13, 815–826 (1983)
Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J.: Fractional Calculus: Models and Numerical Methods. World Scientific, Hackensack (2017)
Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Hackensack (2001)
Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
Stamova, I.M., Stamov, G.T.: Functional and Impulsive Differential Equations of Fractional Order: Qualitative Analysis and Applications. CRC Press/Taylor and Francis Group, Boca Raton (2017)
Ke, Y., Miao, C.: Stability analysis of fractional-order Cohen-Grossberg neural networks with time delay. Int. J. Comput. Math. 92(6), 1102–1113 (2015)
Pratap, A., Raja, R., Cao, J., Lim, C.P., Bagdasar, O.: Stability and pinning synchronization analysis of fractional order delayed Cohen-Grossberg neural networks with discontinuous activations. Appl. Math. Comput. 359, 241–260 (2019)
Rajivganthi, C., Rihan, F.A., Lakshmanan, S., Muthukumar, P.: Finite-time stability analysis for fractional-order Cohen-Grossberg BAM neural networks with time delays. Neural Comput. Appl. 29, 1309–1320 (2018). https://doi.org/10.1007/s00521-016-2641-9
Bai, C.: Stability analysis of Cohen-Grossberg BAM neural networks with delays and impulses. Chaos, Solitons Fractals 35, 263–267 (2008)
Li, K., Zeng, H.: Stability in impulsive Cohen-Grossberg-type BAM neural networks with time-varying delays: a general analysis. Math. Comput. Simul. 80, 2329–2349 (2010)
Li, X.: Exponential stability of Cohen-Grossberg-type BAM neural networks with time-varying delays via impulsive control. Neurocomputing 73, 525–530 (2009)
Stamov, G., Stamova, I., Simeonov, S., Torlakov, I.: On the stability with respect to h-manifolds for Cohen-Grossberg-type bidirectional associative memory neural networks with variable impulsive perturbations and time-varying delays. Math. (MDPI) 8, 335 (2020)
Haddad, W.M., Chellaboina, V.S., Nersesov, S.G.: Impulsive and Hybrid Dynamical Systems, Stability, Dissipativity, and Control. Princeton University Press, Princeton (2006)
Liu, X., Zhang, K.: Impulsive Systems on Hybrid Time Domains. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-06212-5
Stamova, I.M., Stamov, G.T.: Applied Impulsive Mathematical Models. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-28061-5
Li, Y., Chen, Y.Q., Podlubny, I.: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl. 59, 1810–1821 (2010)
Liu, B., Liu, X., Liao, X.: Robust stability of uncertain impulsive dynamical systems. J. Math. Anal. Appl. 290, 519–533 (2004)
Stamov, G.T., Stamova, I.M., Cao, J.: Uncertain impulsive functional differential systems of fractional order and almost periodicity. J. Franklin Inst. 355(12), 5310–5323 (2018)
Chen, T., Rong, L.: Robust global exponential stability of Cohen-Grossberg neural networks with time delays. IEEE Trans. Neural Netw. 15(1), 203–206 (2004)
Wan, Y., Cao, J., Wen, G., Yu, W.: Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks. Neural Netw. 73, 86–94 (2016)
Yuan, K., Cao, J., Li, H.-X.: Robust stability of switched Cohen-Grossberg neural networks with mixed time-varying delays. IEEE Trans Syst. Man Cybern. 36(6), 1356–1363 (2006)
Acknowledgements
This research was funded in part by the European Regional Development Fund through the Operational Program “Science and Education for Smart Growth” under contract UNITe No BG05M2OP001–1.001–0004 (2018–2023).
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Stamova, I., Sotirov, S., Simeonov, S., Stamov, G. (2022). Effects of Variable Impulsive Perturbations on the Stability of Fractional-Order Cohen–Grossberg Neural Networks with Respect to Functions. In: Sotirov, S.S., Pencheva, T., Kacprzyk, J., Atanassov, K.T., Sotirova, E., Staneva, G. (eds) Contemporary Methods in Bioinformatics and Biomedicine and Their Applications. BioInfoMed 2020. Lecture Notes in Networks and Systems, vol 374. Springer, Cham. https://doi.org/10.1007/978-3-030-96638-6_20
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DOI: https://doi.org/10.1007/978-3-030-96638-6_20
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