Fractional order uncertain BAM neural networks with mixed time delays: An existence and Quasi-uniform stability analysis
Abstract
This research investigates the presence of unique solutions and quasi-uniform stability for a class of fractional-order uncertain BAM neural networks utilizing the Banach fixed point concept, the contraction mapping principle, and analysis techniques. In order to guarantee the equilibrium point of fractional-order BAM neural networks with undetermined parameters, some new adequate criteria are devised, and both time delays result in quasi-uniform stability. The acquired results, which are simple to verify in practice, enhance and extend several earlier research works in some ways. Finally, two illustrative examples are provided to show the value of the suggested outcomes.
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References
1. Alofi A., Cao J., Elaiw A., Al-Mazrooei A. Delaydependent stability criterion of Caputo fractional neural networks with distributed delay, Discrete Dynamics in Nature and Society (2014), Article ID 529358, pp. 6.
2. Arena P., Caponetto R., Fortuna L. and Porto D., Bifurcation and chaos in non-integer order cellular neural networks, International Journal of Bifurcation and Chaos 8 (1998), 1527–1539.
3. Arik S. and Tavsanoglu V., Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays, Neurocomputing 68 (2005), 161–176.
4. Banach S., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 3 (1922), 133–181.
5. Bao H. and Cao J., Projective synchronization of fractional-order memristor-based neural networks, Neural Networks 63 (2015), 1–9.
6. Bao H., Park J. and Cao J., Adaptive synchronization of fractional-order memristor-based neural networks with time delay, Nonlinear Dynamics 82 (2015), 1343–1354.
7. Butzer P.L., Westphal U. An introduction to fractional calculus in physics, World Scientific, Singapore (2000).
8. Cao J. and Wang J., Global asymptotic and robust stability of recurrent neural networks with time delays, IEEE Transactions on Circuits & Systems I Regular Papers 52 (2005), 417–426.
9. Cao J. and Wang L., Exponential Stability and periodic oscillatory solution in BAM networks with delays, IEEE Transaction on Neural Networks 13 (2002), 457–463.
10. Cao Y., Bai C. Finite-time stability of fractionalorder BAM neural networks with distributed delay, Abstract and Applied Analysis (2014), Article ID 634803, pp. 8.
11. Cao Y. and Bai C., Existence and stability analysis of fractional order BAM neural networks with a time delay, Applied Mathematics 6 (2015), 2057–2068.
12. Chen L., Chai Y., Wu R., Ma T. and Zhai H., Dynamic analysis of a class of fractional-order neural networks with delay, Neurocomputing 111 (2013), 190–194.
13. Corduneanu C. Principles of differential and integral equations, Allyn and Bacon, MA, USA 1971.
14. Gu R.C., Xu Y. Chaos in a fractional-order dynamical model of love and its control, Nonlinear Mathematics for Uncertainty & Its Applications, Nl-mua, Beijing, China, September. DBLP (2011), 349–356.
15. Hilfer R. Applications of fractional calculus in physics world scientific, Hackensack, NJ 2001.
16. Hu M., Cao J. and Hu A., Exponential stability of discretetime recurrent neural networks with time-varying delays in the leakage terms and linear fractional uncertainties, IMA Journal of Mathematical Control and Information 31 (2014), 345–362.
17. Huang C., Cao J. and Xiao M., Hybrid control on bifurcation for a delayed fractional gene regulatory network, Chaos, Solitons & Fractals 87 (2016), 19–29.
18. Huang H., Huang T.W. and Chen X.P., A mode-dependent approach to state estimation of recurrent neural networks with Markovian jumping parameters and mixed delays, Neural Networks 46 (2013), 50–61.
19. Jmal A., Ben Makhlouf A., Nagy A.M. and Naifar O., Finite-time stability for Caputo-Katugampola fractional-order time-delayed neural networks, Neural Processing Letters 50(1) (2019), 607–621.
20. Kilbas A., Srivastava M.H. and Trujillo J.J., Theory and application of Fractional differential equations, in: North Holland Mathematics Studies 204 (2006).
21. Kosko B., Adaptive bidirectional associative memories, Applied Optics 26 (1987), 4947–4960.
22. Kosko B. Neural networks and fuzzy systems-a dynamical system approach to machine intelligence, Prentice Hall, Englewood Cliffs, NJ, USA 1992.
23. Kuczma M. An introduction to the theory of fractional equations and inequalities: Cauchy ′s equation and Jensen ′s inequality, Birkhauser (2009).
24. Li C.P. and Deng W.H., Remarks on fractional derivatives, Applied Mathematics and Computation 187 (2007), 777–784.
25. Li R. and Cao J., Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term, Applied Mathematics and Computation 278 (2016), 54–69.
26. Li P.L., Lu Y.J., Xu C.J., Ren J. Insight into Hopf bifurcation and control methods in fractional order BAM neural networks incorporating symmetric structure and delay, Cognitive Computation (2023)
27. Li X. and Rakkiyappan R., Stability results for Takagi-Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term, Neural Computing & Applications 22 (2013), 203–219.
28. Li X. and Song S., Stabilization of delay systems: delaydependent impulsive control, IEEE Transactions on Automatic Control 62(1) (2017), 406–411.
29. Li X. and Song S., Impulsive control for existence, uniqueness andglobal stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays, IEEE Transactions on Neural Networks and Learning Systems 24 (2013), 868–877.
30. Li X. and Wu J., Stability of nonlinear differential systems with state-dependent delayed impulses, Automatica 64 (2016), 63–69.
31. Li X., Zhu Q. and Regan D.O., pth moment exponential stability of impulsive stochastic functional differential equations andapplication to control problems of NNs, Journal of the Franklin Institute 351 (2014), 4435–4456.
32. Liu X., Jiang N., Cao J., Wang S. and Wang Z., Finite-time stochastic stabilization for BAM neural networks with uncertainties, Journal of the Franklin Institute 350 (2013), 2109–2123.
33. Liu H., Li S., Wang H., Huo Y. and Luo J., Adaptive synchronization for a class of uncertain fractional-order neural networks, Entropy 17 (2015), 185–200.
34. Lundstrom B.N., Higgs M.H., Spain W.J. and Fairhall A.L., Fractional differentiation by neocortical pyramidal neurons, Nature Neuroscience 11 (2008), 1335–1342.
35. Maharajan C., Raja R., Cao J. and Rajchakit G., Novel global robust exponential stability criterion for uncertain inertial-type BAMneural networks with discrete and distributed time-varying delays via Lagrange sense, Journal of the Franklin Institute 355(11) (2018), 4727–4754.
36. Maharajan C. and Sowmiya C., Exponential stability of delay dependent neutral-type descriptor neural networks with uncertain parameters, Franklin Open 100042 (2023). https://doi.org/10.1016/j.fraope.2023.100042
37. Maharajan C., Raja R., Cao J., Ravi G. and Rajchakit G., Global exponential stability of Markovian jumping stochastic impulsive uncertain BAM neural networks with leakage, mixed time delays, and a-inverse Hölder activation functions, Advances in Difference Equations 113 (2018).
38. Meyer-Base A., Roberts R. and Thummler V., Local uniform stability of competitive neural networks with different timescales under vanishing perturbations, Neurocomputing 73 (2010), 770–775.
39. Mitrinovic S. Analytic Inequalities, Springer-Verlag, New York 1970.
40. Naifar O., Jmal A., Nagy A.M., Ben A. Improved Quasi uniform stability for fractional order neural nets with mixed delay, Mathematical Problems in Engineering Article ID 8811226, (2020) pp. 7.
41. Ou W., Xu C.J., Cui Q., Liu Z., Pang Y., Farman M., Ahmad S., Zeb A. Mathematical study on bifurcation dynamics and control mechanism of tri-neuron BAM neural networks including delay, Mathematical Methods in the Applied Sciences (2023), https://doi.org/10.1002/mma.9347.
42. Park J., A novel criterion for global asymptotic stability of BAM neural networks with time delays, Chaos, Solitons and Fractals 29 (2006), 446–453.
43. Podlubny I. Fractional differential equations, Academic, New York 1999.
44. Raja R., Sakthivel R. and Marshal S., Anthoni, Linear matrix inequality approach to stochastic stability of uncertain delayed BAM neural networks, IMA Journal of Applied Mathematics 78 (2012), 1156–1178.
45. Raja R., Zhu Q., Senthilraj S. and Samidurai R., Improved stability analysis of uncertain neutral type neural networks with leakage delays and impulsive effects, Applied Mathematics and Computation 266 (2015), 1050–1069.
46. Rakkiyappan R., Cao J. and Velmurugan G., Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays, IEEE Transaction on Neural Networks and Learning Systems 26 (2014), 84–97.
47. Rakkiyappan R., Sivaranjani R., Velmurugan G. and Cao J., Analysis of global O(t-α) stability and global asymptotical periodicity for a class of fractional-order complex-valued neural networks with time varying delays, Neural Networks 77 (2016), 51–69.
48. Ren F., Cao F. and Cao J., Mittag-Leffler stability and generalized Mittag-Leffler stability of fractional-order gene regulatory networks, Neurocomputing 160 (2015), 185–190.
49. Song C. and Cao J., Dynamics in fractional-order neural net-works, Neurocomputing 142 (2014), 494–498.
50. Song L., Xu S.Y. and Yang J.Y., Dynamical models of happiness with fractional order, Communications in Nonlinear Science and Numerical Simulation 15(3) (2010), 616–628.
51. Srivastava H.M., Abbas S., Tyagi S. and Lassoued D., Global exponential stability of fractional-order impulsive neural network with time-varying and distributed delay, Mathematical Methods in Applied Sciences 41 (2018), 2095–2104.
52. Tu Z., Cao J. and Hayat T., Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks, Neural Networks 75 (2016), 47–55.
53. Tu Z., Wang L., Zha Z. and Jian J., Global dissipativity of a class of BAM neural networks with time-varying and unbound delays, Communications in Nonlinear Science & Numerical Simulation 18 (2013), 2562–2570.
54. Velmurugan G., Rakkiyappan R. and Cao J., Finite-time synchronization of fractional-order memristor-based neural networks with time delays, Neural Networks 73 (2016), 36–46.
55. Wan L., Zhan X., Gao H., Yang Q., Han T. and Ye M., Multiple asymptotical stability analysis for fractional-order neural networks with time delays, International Journal of Systems Science 50(10) (2019), 2063–2076.
56. Wu H., Zhang X., Xue S. and Niu P., Quasi-uniform stability of Caputo-type fractional-order neural networks with mixed delay, International Journal of Machine Learning and Cybernetics 8(5) (2017), 1501–1511.
57. Xiao M., Zheng W., Jiang G. and Cao J., Undamped oscillations generated by Hopf bifurcations in fractional order recurrent neural networks with Caputoderivative, IEEE Transactions on Neural Networks and Learning Systems 26(12) (2015), 3201–3214.
58. Xu C.J., Mu D., Pan Y., Aouiti C. and Yao L., Exploring bifurcation in a fractional-order predator-prey system with mixed delays, Journal of Applied Analysis and Computation 13(3) (2023), 1119–1136.
59. Zhang R., Qi D. and Wang Y., Dynamics analysis of fractional order three-dimensional Hopfield neural network, In International conference on natural computation (2010), 3037–3039.
60. Zhang H., Ye R., Liu S., Cao J., Alsaedi A. and Li X., LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays, International Journal of Systems Science 49(3) (2018), 537–545.
61. Zhou S., Li H. and Zhu Z., Chaos control and synchronization in a fractional neuron network system, Chaos, Solitons and Fractals 36 (2008), 973–984.
62. Zhou S., Lin X., Zhang L., Li Y. Chaotic synchronization of a fractional neurons network system with two neurons, In International conference on communications, circuits and systems (2010), 773–776.
63. Zhu H., Zhou S., Zhang W. Chaos and synchronization of time-delayed fractional neuron network system, In The 9th international conference for Young computer scientists (2008), 2937–2941.
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Article first published online: January 3, 2024
Issue published: February 14, 2024
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