Existence and global exponential stability of anti-periodic solutions for generalised inertial competitive neural networks with time-varying delays

References

• Amari, S.-I. (1982). Competitive and cooperative aspects in dynamics of neural excitation and self-organization. In Amari, S. & Arbib, M.-A., eds. Competition and cooperation in neural nets (pp. 1–28). Berlin, Heidelberg: Springer.
   Google Scholar
• Amster, P. (2013). Topological methods in the study of boundary value problems. New York, NY: Springer.
   Google Scholar
• Angelaki, D. E., & Correia, M. J. (1991). Models of membrane resonance in pigeon semicircular canal type II hair cells. Biological Cybernetics, 65(1), 1–10.
   PubMed Web of Science ®Google Scholar
• Ashmore, J. F., & Attwell, D. (1985). Models for electrical tuning in hair cells. Proceedings of the Royal Society of London B, 226(1244), 325–344.
   Google Scholar
• Babcock, K. L., & Westervelt, R. M. (1986). Stability and dynamics of simple electronic neural networks with added inertia. Physica D: Nonlinear Phenomena, 23(1–3), 464–469.
   Google Scholar
• Cao, J., & Wan, Y. (2014). Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Networks, 53, 165–172.
   PubMed Web of Science ®Google Scholar
• Chaouki, A., Abed, A. E., Cao, J., & Ahmed, A. (2018). Stability analysis for a class of impulsive competitive neural networks with leakage time-varying delays. Science China Technological Sciences, 61(9), 1384–1403.
   Web of Science ®Google Scholar
• Cohen, M. A., & Grossberg, S. (1983). Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man, and Cybernetics, 5, 815–826.
   Google Scholar
• Du, B. (2018). Stability analysis of periodic solution for a complex-valued neural networks with bounded and unbounded delays. Asian Journal of Control, 20(2), 881–892.
   Web of Science ®Google Scholar
• Du, B., Lian, X., & Cheng, X. (2018). Partial differential equation modeling with Dirichlet boundary conditions on social networks. Boundary Value Problems, 2018(1), 50.
   Google Scholar
• Du, B., Zhang, W., & Yang, Q. (2017). Robust state estimation for neutral-type neural networks with mixed time delays. Journal of Nonlinear Sciences and Applications, 10(5), 2565–2578.
   Google Scholar
• Engel, P. M., & Molz, R. F. (n.d.). A new proposal for implementation of competitive neural networks in analog hardware. In Proceedings of the 5th brazilian symposium on neural networks, Belo Horizonte, Brazil, (pp. 186–191).
   Google Scholar
• Gan, Q., Hu, R., & Liang, Y. (2012). Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays. Communications in Nonlinear Science and Numerical Simulation, 17(9), 3708–3718.
   Web of Science ®Google Scholar
• Gong, S., Yang, S., Guo, Z., & Huang, T. (2018). Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller. Neural Networks, 102, 138–148.
   PubMed Web of Science ®Google Scholar
• Gu, H., Jiang, H., & Teng, Z. (2010). Existence and global exponential stability of equilibrium of competitive neural networks with different time scales and multiple delays. Journal of the Franklin Institute, 347(5), 719–731.
   Web of Science ®Google Scholar
• He, X., Li, C., & Shu, Y. (2012). Bogdanov-Takens bifurcation in a single inertial neuron model with delay. Neurocomputing, 89, 193–201.
   Web of Science ®Google Scholar
• Ke, Y., & Miao, C. (2013). Stability and existence of periodic solutions in inertial BAM neural networks with time delay. Neural Computing and Applications, 23(3–4), 1089–1099.
   Web of Science ®Google Scholar
• Ke, Y., & Miao, C. (2017). Anti-periodic solutions of inertial neural networks with time delays. Neural Processing Letters, 45(2), 523–538.
   Web of Science ®Google Scholar
• Li, H., Li, C., Zhang, W., & Xu, J. (2018). Global dissipativity of inertial neural networks with proportional delay via new generalized halanay inequalities. Neural Processing Letters, 48(3), 1543–1561.
   Web of Science ®Google Scholar
• Li, Y., Qin, J., & Li, B. (2019a). Anti-periodic solutions for quaternion-valued high-order Hopfield neural networks with time-varying delays. Neural Processing Letters, 49, 1217–1237.
   Web of Science ®Google Scholar
• Li, Y., Qin, J., & Li, B. (2019b). Existence and global exponential stability of anti-periodic solutions for delayed quaternion-valued cellular neural networks with impulsive effects. Mathematical Methods in the Applied Sciences, 42(1), 5–23.
   Web of Science ®Google Scholar
• Li, Y., & Shu, J. (2011). Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. Communications in Nonlinear Science and Numerical Simulation, 16(8), 3326–3336.
   Web of Science ®Google Scholar
• Li, Y., & Yang, L. (2009). Anti-periodic solutions for Cohen-Grossberg neural networks with bounded and unbounded delays. Communications in Nonlinear Science and Numerical Simulation, 14(7), 3134–3140.
   Web of Science ®Google Scholar
• Li, Y., Yang, L., & Wu, W. (2015). Anti-periodic solution for impulsive BAM neural networks with time-varying leakage delays on time scales. Neurocomputing, 149, 536–545.
   Web of Science ®Google Scholar
• Liao, H., Zhang, Z., Ren, L., & Peng, W. (2017). Global asymptotic stability of periodic solutions for inertial delayed BAM neural networks via novel computing method of degree and inequality techniques. Chaos, Solitons & Fractals, 104, 785–797.
   Web of Science ®Google Scholar
• Liu, Q., Liao, X., Guo, S., & Wu, Y. (2009). Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation. Nonlinear Analysis: Real World Applications, 10(4), 2384–2395.
   Web of Science ®Google Scholar
• Liu, Q., Liao, X., Guo, S., & Yu, W. (2009). Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation. Nonlinear Analysis: Real World Applications, 10(4), 2384–2395.
   Web of Science ®Google Scholar
• Liu, Q., Liao, X., Liu, Y., Zhou, S., & Guo, S. (2009). Dynamics of an inertial two-neuron system with time delay. Nonlinear Dynamics, 58(3), 573–609.
   Web of Science ®Google Scholar
• Liu, Q., Liao, X., Yang, D., & Guo, S. (2007). The research for Hopf bifurcation in a single inertial neuron model with external forcing. In IEEE international conference on granular computing, Fremont, CA, USA, (pp. 528–533).
   Google Scholar
• Liu, Y., Yang, Y., Liang, T., & Li, L. (2014). Existence and global exponential stability of anti-periodic solutions for competitive neural networks with delays in the leakage terms on time scales. Neurocomputing, 133(8), 471–482.
   Google Scholar
• Liu, Y., Zhang, D., Lou, J., Lu, J., & Cao, J. (2018). Stability analysis of quaternion-valued neural networks: Decomposition and direct approaches. IEEE Transactions on Neural Networks and Learning Systems, 29(9), 4201–4211.
   PubMed Web of Science ®Google Scholar
• Liu, Y., Zhang, D., Lu, J., & Cao, J. (2016). Global µ-stability criteria for quaternion-valued neural networks with unbounded time-varying delays. Information Sciences, 360, 273–288.
   Web of Science ®Google Scholar
• Long, Z. (2016). New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms. Neurocomputing, 171, 503–509.
   Web of Science ®Google Scholar
• Meyer-Bäse, A., Ohl, F., & Scheich, H. (1996). Singular perturbation analysis of competitive neural networks with different time scales. Neural Computation, 8(8), 1731–1742.
   PubMed Web of Science ®Google Scholar
• Meyer-Bäse, A., Pilyugin, S. S., & Chen, Y. (2003). Global exponential stability of competitive neural networks with different time scales. IEEE Transactions on Neural Networks, 14(3), 716–719.
   PubMedGoogle Scholar
• Meyer-Bäse, A., Roberts, R., & Thümmler, V. (2010). Local uniform stability of competitive neural networks with different time-scales under vanishing perturbations. Neurocomputing, 73(4–6), 770–775.
   Web of Science ®Google Scholar
• Miao, C., & Ke, Y. (2014). Exponential stability of periodic solutions for inertial type BAM Cohen-Grossberg neural networks. Abstract and Applied Analysis, 2014, 19. Article ID 857341.
   Google Scholar
• Nie, X., & Cao, J. (2012). Existence and global stability of equilibrium point for delayed competitive neural networks with discontinuous activation functions. International Journal of Systems Science, 43(3), 459–474.
   Web of Science ®Google Scholar
• Okochi, H. (1988). On the existence of periodic solutions to nonlinear abstract parabolic equations. Journal of the Mathematical Society of Japan, 40(1988), 541–553.
   Google Scholar
• Sowmya, B., & Rani, B. S. (2011). Colour image segmentation using fuzzy clustering techniques and competitive neural network. Applied Soft Computing, 11(3), 3170–3178.
   Web of Science ®Google Scholar
• Tu, Z., Cao, J., Alsaedi, A., & Alsaadi, F. (2017). Global dissipativity of memristor-based neutral type inertial neural networks. Neural Networks, 88, 125–133.
   PubMed Web of Science ®Google Scholar
• Tu, Z., Cao, J., & Hayat, T. (2016). Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays. Neurocomputing, 171, 524–531.
   Web of Science ®Google Scholar
• Wei, X., & Qiu, Z. (2013). Anti-periodic solutions for BAM neural networks with time delays. Applied Mathematics and Computation, 221, 221–229.
   Web of Science ®Google Scholar
• Xu, C. (2018). Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays. Mathematics and Computers in Simulation, 149, 69–90.
   Web of Science ®Google Scholar
• Xu, C., & Chen, L. (2018). Effect of leakage delay on the almost periodic solutions of fuzzy cellular neural networks. Journal of Experimental & Theoretical Artificial Intelligence, 30(6), 993–1011.
   Web of Science ®Google Scholar
• Xu, C., Chen, L., & Guo, T. (2018). Anti-periodic oscillations of bidirectional associative memory (BAM) neural networks with leakage delays. Journal of Inequalities and Applications, 2018, 68.
   PubMedGoogle Scholar
• Xu, C., & Li, P. (2016). Existence and exponentially stability of anti-periodic solutions for neutral BAM neural networks with time-varying delays in the leakage terms. Journal of Nonlinear Science and Applications, 9(3), 1285–1305.
   Google Scholar
• Xu, C., & Li, P. (2018). Global exponential convergence of fuzzy cellular neural networks with leakage delays, distributed delays and proportional delays. Circuits, Systems, and Signal Processing, 37(1), 163–177.
   Web of Science ®Google Scholar
• Xu, C., Li, P., & Pang, Y. (2016). Exponential stability of almost periodic solutions for memristor-based neural networks with distributed leakage delays. Neural Computation, 28(12), 2726–2756.
   PubMed Web of Science ®Google Scholar
• Xu, C., Pang, Y., & Li, P. (2016). Anti-periodic solutions of Cohen-Grossberg shunting inhibitory cellular neural networks on time scales. Journal of Nonlinear Science and Applications, 9(5), 2376–2388.
   Google Scholar
• Xu, C., & Zhang, Q. (2015). Existence and global exponential stability of anti-periodic solutions for BAM neural networks with inertial term and delay. Neurocomputing, 153, 108–116.
   Web of Science ®Google Scholar
• Yu, S., Zhang, Z., & Quan, Z. (2015). New global exponential stability conditions for inertial Cohen-Grossberg neural networks with time delays. Neurocomputing, 151(Part 3), 1446–1454.
   Google Scholar
• Zhang, D., Kou, K. I., Liu, Y., & Cao, J. (2017). Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field. Neural Networks, 94, 55–66.
   PubMed Web of Science ®Google Scholar
• Zhang, G., Zeng, Z., & Hu, J. (2018). New results on global exponential dissipativity analysis of memristive inertial neural networks with distributed time-varying delays. Neural Networks, 97, 183–191.
   PubMed Web of Science ®Google Scholar
• Zhou, Q. (2016). Anti-periodic solutions for cellular neural networks with oscillating coefficients in leakage terms. International Journal of Machine Learning and Cybernetics, 8(5), 1607–1613.
   Web of Science ®Google Scholar