Abstract
In this chapter, analytical results are derived for CNN models with memristor synapses (M-CNN) in which neurons operate in a regime called edge-of-chaos. The systems describing the models under consideration consist of highly nonlinear differential equations. We propose new algorithms based on the generalized local activity scheme for the determination of the edge-of-chaos regime in M-CNN. MATLAB implementation of algorithms based on a numerical integration of the M-CNN state equations allowing a reliable and accurate determination of the edge-of-chaos parameter regime is proposed. Applications of the obtained results for noise removing are presented. New M-CNN model arising in nano-structures is proposed. The model consists of 2D dynamic coupled problem in multifunctional nano-heterogeneous piezoelectric composites. Simulations and validation are presented for transversely isotropic piezoelectric material PZT4.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Chua LO, Yang L (1988) Cellular neural network: theory and applications. IEEE Trans CAS 35:1257
Chua LO, Kang SM (1976) Memristive devices and systems. Proc IEEE 64(2):209–223
Chua LO (2005) Local activity is the origin of complexity. Int J Bifurc Chaos 15(11):3435–3456
Dineva P, Gross DR, Müller R, Rangelov T (2014) Dynamic fracture of piezoelectric materials. In: Solutions of time-harmonic problems via BIEM, solid mechanics and its applications, vol 212. Springer International Publishing, Switzerland
Fang XQ, Lin JX, Dou LH, Chen MZ (2012) Dynamic strength around two interactive piezo-electric nano-fibers with surfaces/interfaces in solid under electro-elastic wave. Thin Solid Films 520:3587–3592
Gurtin ME, Murdoch AI (1975) A continuum theory of elastic material surfaces. Arch Ration Mach Anal 57:291–323
Jammes M, Mogilevskaya SG, Crouch SL (2009) Multiple circular nano-inhomogeneities and/or nano-pores in one of two joint isotropic half-planes. Eng Anal Bound Elem 33:233–248
Mazumder P, Li S-R, Ebong IE (2009) Tunneling-based cellular nonlinear network architectures for image processing. In: IEEE transactions on very large scale integration (VLSI) systems, vol 17, no 4, pp 487–495
Perona P, Malik J (1987) Scale space and edge detection using anisotropic diffusion. In: Proceedings of IEEE computer society: workshop and computer vision, pp 16–22
Shih Y, Elman HC (1998) Modified streamline diffusion schemes for convection—diffusion problems. Int J Bifurc Chaos
Slavova A (2003) Cellular neural networks: dynamics and modeling. Kluwer Academic Publishers
Slavova A, Tetzlaff R (2018) Memristor CNNs with hysteresis. In: Studies in computational intelligence, vol 793. Springer, pp 383–394
Slavova A, Tetzlaff R, Zafirova Z (2019) Edge of chaos in nanoscale memristor CNN. In: IEEE Proceedings of the ISCAS 2019
Slavova A (2020) Dynamics of a new hysteresis memristor CNN. In: IEEE Proceedings of the ECCTD 2020
Slavova A, Tetzlaff T (2019) Mathematical analysis of memristor CNN. In: ItechOpen. https://doi.org/10.5772/intechopen.86446
Slavova A (2019) Local activity in reaction-diffusion CNN models. In: AIP conference proceedings, vol 2159, 030030-1-11
Slavova A (1998) Dynamic properties of cellular neural networks with nonlinear output function. IEEE Trans CAS I 45(5):587–590
Slavova A (1998) Generalization of CNN with hysteresis nonlinearity. In: Proceedings of the IEEE, international workshop on CNNA, pp 55–61
Slavova A (2001) Stability analysis of cellular neural networks with nonlinear dynamics. Nonlinear Anal: R. World Appl 2(1):93–103
Slavova A (2006) Dynamics and travelling waves in CNN vector disease model. IEEE Trans CAS—II 53(11):1304–1307
Vidyasagar M (2002) Nonlinear systems analysis, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia
Vladimirov V (1971) Equations of mathematical physics. Marcel Dekker Inc., New York
Weickert J (1997) A review of nonlinear diffusion filtering. In: Lecture notes in computer science, vol 1252. Springer, Berlin, pp 3–28
Weickert J, Benhamouda B (1996) Nonlinear diffusion scale-spaces: from the continuous to the discrete setting. In: Berger MO, et al (eds) Proceedings of the ICAOS96: images, wavelets and PDEs, vol 219. Springer, New York, pp 111–118
Acknowledgements
We acknowledge the provided access to the e-infrastructure of the Centre for Advanced Computing and Data Processing, with the financial support by the Grant No BG05M2OP001-1.001-0003, financed by the Science and Education for Smart Growth Operational Program (2014–2020) and co-financed by the European Union through the European structural and Investment funds. The author was supported by the project TE 257/25-1 between DFG and Bulgarian Academy of Sciences.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Slavova, A., Litsyn, E. (2022). Edge-of-Chaos in CNN Models with Memristor Synapses. In: Chua, L.O., Tetzlaff, R., Slavova, A. (eds) Memristor Computing Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-90582-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-90582-8_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-90581-1
Online ISBN: 978-3-030-90582-8
eBook Packages: EngineeringEngineering (R0)