## THERMAL SCIENCE

International Scientific Journal

### ANTI-PERIODIC SOLUTIONS FOR FRACTIONAL-ORDER BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DELAYS

**ABSTRACT**

This paper concerns fractional-order bidirectional associative memory (BAM) neural networks (NN) with distributed delays. Based on inequality technique and Lyapunov functional method, some novel sufficient conditions are obtained for the existence and exponential stability of anti-periodic (AP) solutions are established. An example is given to show the feasibility main results.

**KEYWORDS**

PAPER SUBMITTED: 2019-08-05

PAPER REVISED: 2019-10-11

PAPER ACCEPTED: 2019-10-15

PUBLISHED ONLINE: 2019-11-02

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Supplement 6**, PAGES [S2169 - S2177]

- Cao, J., Wang, L., Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Transactions on Neural Networks, 13 (2002), 2, pp. 457-463
- Park, J. H., A novel criterion for global asymptotic stability of BAM neural networks with time delays, Chaos, Solitons and Fractals, 29 (2006), 2, pp. 446-453
- Ho, D. W., et al., Global exponential stability of impulsive high-order BAM neural networks with time-varying delays, Neural Networks, 19 (2006), 10, pp. 1581-1590
- Song, Q., Cao, J., Global exponential stability of bidirectional associative memory neural networks with distributed delays, Abstract and Applied Analysis 15 Journal of Computational and Applied Mathematics, 202 (2007), 2, pp. 266-279
- Lou, X., Cui, B., New criteria on global exponential stability of BAM neural networks with distributed delays and reactiondiffusion terms, International Journal of Neural Systems, 17 (2007), 1, pp. 43-52
- Balasubramaniam, P., Rakkiyappan, R., Global exponential stability for neutral-type BAM neural networks with timevarying delays, International Journal of Computer Mathematics, 87 (2010), 9, pp. 2064-2075
- Wang, Y., Cao, J., Exponential stability of stochastic higher-order BAM neural networks with reaction-diffusion terms and mixed time-varying delays, Neurocomputing, 119 (2013), pp. 192- 200
- Zhang, A., et al., Existence and global exponential stability of periodic solution for high- with leakage delays and probabilistic time-varying delays, Applied Mathematics and Computation, 219 (2013), 17, pp. 9408-9423
- Podlubny, I., Fractional Differential Equations, Mathematics in Science and Engineering, Technical University of Kosice, Kosice, Slovakia, 1999.
- Diethelm, K., The Analysis of Fractional Differential Equations, Springer, Berlin, Germany, 2010.
- Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, North- Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006.
- Arena, P., et al., Chaotic behavior in noninteger-order cellular neural networks, Physical Review E, 61 (2000) 1, pp. 776-781
- Boroomand, A., Menhaj, M.B., Fractional-order Hopfield neural networks, in Advances in Neuro- Information Processing, 2009, Vol.5506, pp. 883-890
- Arena, P., et al., Bifurcation and chaos in noninteger order cellular neural networks, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 8 (1998),7, pp. 1527- 1539
- Delavari, H., et al., Stability analysis of Caputo fractional-order nonlinear systems revisited, Nonlinear Dynamics, 67 (2012), 4, pp. 2433-2439
- Li, Y., et al., Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability, Computers & Mathematics with Applications, 59 (2010), 5, pp. 1810-1821
- Kaslik, E., Sivasundaram, S., Dynamics of fractional-order neural networks, in Proceedings of the International Joint Conference on Neural Network (IJCNN -11), 2011, pp. 611-618
- Kaslik, E., Sivasundaram, S., Nonlinear dynamics and chaos in fractional-order neural networks, Neural Networks, 32 (2012), pp. 245-256
- Wu, R. C., et al., Finite-time stability of fractional-order neural networks with delay, Communications in Theoretical Physics, 60 (2013), 2, pp. 189-193
- Alofi, A., et al., Delay-dependent stability criterion of Caputo fractional neural networks with distributed delay, Discrete Dynamics in Nature and Society, 2014 (2014), Article ID 529358, 6 pages
- Hopfield, J. J., Neurons with graded response have collective computational properties like those of two-state neurons, Proceedings of the National Academy of Sciences of the United States of America, 81 (1984), 10, pp. 3088-3092
- Kosko, B., Bidirectional associative memories, IEEE Transactions on Systems, Man, and Cybernetics, 18 (1988), 1, pp. 49-60
- Arik, S., Tavsanoglu, V., Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays, Neurocomputing, 68 (2005), 1-4, pp. 161-176
- Senan, S., et al., New robust stability results for bidirectional associative memory neural networks with multiple time delays, Applied Mathematics and Computation, 218 (2012), 23, pp. 11472-11482
- Liu, B., Global exponential stability for BAM neural networks with time-varying delays in the leakage terms, Nonlinear Analysis: Real World Applications, 14 (2013), 1, pp. 559-566
- Rajaand, R., Anthony, S.M., Global exponential stability of BAM neural networks with timevarying delays: the discrete- time case, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 2, pp. 613-622