-
Mathematical Biosciences and Engineering, 2019, 16(3): 1210-1227. doi: 10.3934/mbe.2019058.
Research article Special Issues
-
Export file:
Format
- RIS(for EndNote,Reference Manager,ProCite)
- BibTex
- Text
Content
- Citation Only
- Citation and Abstract
Stability properties of neural networks with non-instantaneous impulses
1 Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
2 Department of Applied Mathematics and Modeling, University of Plovdiv ”Paisii Hilendarski”, 4000 Plovdiv, Bulgaria
3 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
4 Distinguished University Professor of Mathematics, Florida Institute of Technology, Melbourne, FL 32901, USA
Received: , Accepted: , Published:
Special Issues: Differential Equations in Mathematical Biology
Keywords: nonlinear neural networks; non-instantaneous impulses; Lipschitz stability
Citation: Ravi Agarwal, Snezhana Hristova, Donal O’Regan, Radoslava Terzieva. Stability properties of neural networks with non-instantaneous impulses. Mathematical Biosciences and Engineering, 2019, 16(3): 1210-1227. doi: 10.3934/mbe.2019058
References:
- 1. R. Agarwal, S. Hristova and D. O'Regan, Non-Instantaneous Impulses in Differential Equations, Springer, 2017.
- 2. H. Akca, R. Alassar, V. Covachev, Z. Covacheva and E. A. Al-Zahrani, Continuous-time additive Hopfield-type neural networks with impulses, J. Math. Anal. Appl., 290 (2004), 436–451.
- 3. H. Akca, R. Alassar, Y. M. Shebadeh and V. Covachev, Neural networks: Modelling with impulsive differential equations, Proc. Dynamical Syst. Appl., (2004), 32–47.
- 4. N. T. Carnevale and M. L. Hines, The NEURON Book, Cambridge, UK, Cambridge University Press, 2009.
- 5. F. M. Dannan and S. Elaydi, Lipschitz stability of nonlinear systems of differential equations, J. Math. Anal. Appl., 113, (1986), 562–577.
- 6. K. Gopalsamy, Stability of artificial neural networks with impulses, Appl. Math. Comput., 154 (2004), 783–813.
- 7. J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. USA, 79 (1982), 2554–2558.
- 8. S. Hristova, Qualitative investigations and approximate methods for impulsive equations, Nova Sci. Publ. Inc., New York, 2009.
- 9. S. Hristova and R. Terzieva, Lipschitz stability of differential equations with non-instantaneous impulses, Adv. Differ. Equ., 2016, 322.
- 10. Y. Huang, H. Zhang and Z. Wang, Dynamical stability analysis of multiple equilibrium points in time-varying delayed recurrent neural networks with discontinuous activation functions, Neurocomputing, 91 (2012), 21–28.
- 11. R. D. King, S. M. Garrett and G. M. Coghill, On the use of qualitative reasoning to simulate and identify metabolic pathways, Bioinformatics, 21 (2005), 2017–2026.
- 12. V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
- 13. X. Li and J.Wu, Stability of nonlinear differential systems with state-dependent delayed impulses, Automatica, 64 (2016), 63–69.
- 14. X. Li and S. Song, Stabilization of Delay Systems: Delay-Dependent Impulsive Control, IEEE Transactions on Automatic Control, 62 (2017), 406–411.
- 15. C. Li and G. Feng, Delay-interval-dependent stability of recurrent neural networks with timevarying delay, Neurocomputing, 72 (2009), 1179–1183.
- 16. X. Li, D. W. C. Ho and J. Cao, Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica, 99 (2019), 361–368.
- 17. W. McCulloch and W. H. Pitts, A logical calculus of the ideas immanent in nervous activity, Bill. Math. Bioph., 5 (1943), 115–133.
- 18. A. Rahimi and B. Recht, Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning, Adv. Neural Information Processing Syst, 21 (2008), 1313–1320.
- 19. R. I. Watson Sr., The great psychologists, J.B. Lippincott Co., New York, 1978.
Reader Comments
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)
Associated material
Metrics
Other articles by authors
Related pages
Tools
your name: * your email: *