Abstract
The content of this chapter is closely linked with the theme treated in Chap. 5. Here we also discuss active lattice systems composed of elements with bistable properties. However, the geometrical architecture of the systems to be used is more sophisticated. We consider here a multilayer lattice architecture, with interacting lattices or layers and hence a 3D geometry or anatomy. Many systems from various areas of science and technology have such multilayer 3D structure. Take, for instance Josephson superlattices consisting of many stacked tunnel junctions, artificial reaction-diffusion dynamical systems using molecular electronics technology, neural networks, layered porous media, Cellular Neural Networks and so on [6.1–5,6.10–16,6.22–24,6.26,6.27]. In spite of significant differences between all these cases we may expect some common hence universal properties associated with the multilayer geometry. The purpose of this chapter is to identify and describe such properties.
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References
Babloyantz, A. and Lourenço, C., “Computation with chaos: A paradigm for cortical activity”, Proc. Natl. Acad. Sci. USA 91 (1994) 9027–9031.
Binczak, S., Elibeck, J. C. and Scott, A. C., “Ephatic coupling of myelinated fibers”, Physica D 148 (2001) 159–179.
Bose, A., “Symmetric and antisymmetric phases in parallel coupled nerve fibers”, SIAM J. Appl. Math. 55 (1995) 1650–1674.
Brindley, J., Holden, A. V. and Palmer, A., A numerical model for reentry in weakly coupled parallel excitable fibres, in Nonlinear Wave Processes in Excitable Media, A. V. Holden, M. Markus and H. G. Othmer (Editors), (Plenum Press, New York, 1991), pp. 123–126.
Haken, H., Principles of Brain Functioning. A Synergetic Approach to Brain Activity, Behavior and Cognition (Springer-Verlag, Berlin, 1996).
Heagy, J. F., Carroll, T. L. and Pecora, L. M., “Synchronous chaos in coupled oscillator systems”, Phys Rev. E 50 (1994) 1874–1885.
Heagy, J. F., Carroll, T. L. and Pecora, L. M., “Experimental and mumerical evidence for riddled basins in coupled chaotic systems”, Phys. Rev. Lett. 73 (1994) 3528–3531.
Heagy, J. F., Carroll, T. L. and Pecora, L. M., “Desynchronization by periodic orbits”, Phys. Rev. E 52 (1995) 1253–1256.
Heagy, J. F., Pecora, L. M. and Carroll, T. L., “Short wavelength bifurcations and size instabilities in coupled oscillator systems”, Phys. Rev. Lett. 74 (1995) 4185–4188.
Hopfield, J. J., “Neural networks and physical systems with emergent collective computational abilities”, Proc. Natl. Acad. Sci. USA 79 (1982) 2554–2558.
Hopfield, J. J., “Pattern recognition computation using action potential timing for stimulus representation”, Nature 376 (1995) 33–36.
Hoppensteadt, F. C. and Izhikevich, E. M., “Synchronization of laser oscillators, associative memory, and optical neurocomputing”, Phys. Rev. E 62 (2000) 4010–4013.
Hoppensteadt, F. C. and Izhikevich, E. M., “Oscillatory neurocomputers with dynamic connectivity”, Phys. Rev. Lett. 82 (1999) 2983–2986.
Keener, J. P., “Homogenization and propagation in the bistable equation”, Physica D 136 (2000) 1–17.
Kladko, K., Mitkov, I. and Bishop, A. R., “Universal scaling of wave propagation failure in arrays of coupled nonlinear cells”, Phys. Rev. Lett. 84 (2000) 4505–4508.
Marquie, P., Comte, J. C. and Bilbault, J. M., “Contour detection using a two-dimensional diffusive nonlinear electrical network”, Proc. 2000 Int. Symposium On Nonlinear Theory and Its Applications (NOLTA 2000, Dresden, Germany, 2000), pp. 331–334.
Nekorkin, V. I., Kazantsev, V. B. and Velarde, M. G., “Image transfer in multilayered assemblies of lattices of bistable oscillators”, Phys. Rev. E 59 (1999) 4515–4522.
Nekorkin, V. I., Kazantsev, V. B. and Velarde, M. G., “Mutual synchronization of two lattices of bistable elements”, Phys. Lett. A 236 (1997) 505–512.
Nekorkin, V. I., Kazantsev, V. B., Artyukhin, D. V. and Velarde, M. G., “Wave propagation along interacting fiber-like lattices”, Eur. Phys. J. B 11 (1999) 677–685.
Nekorkin, V. I., Kazantsev, V. B., Rabinovich, M. I. and Velarde, M. G., “Controlled disordered patterns and information transfer between coupled neural lattices with oscillatory states”, Phys. Rev. E 57 (1998) 3344–3351.
Nekorkin, V. I., Kazantsev, V. B., Velarde, M. G. and Chua, L. O., “Pattern interaction and spiral waves in a two-layer system of excitable units”, Phys. Rev. E 58 (1998) 1764–1773.
Palmer, A., Brindley, J. and Holden A. V., “Initiation and stability of reentry in two coupled excitable fibers”, Bull. Math. Biology 54 (1992) 1039–1056.
Panfilov, A. V. and Holden A. V., “Vortices in a system of two coupled excitable fibers”, Phys. Lett. A 147 (1990) 463–466.
Pecora, L. M. and Carroll, T. L., “Synchronization of chaotic systems”, Phys. Rev. Lett. 64 (1990) 821–824.
Velarde, M. G., Nekorkin, V. I., Kazantsev, V. B. and Ross, J., “The emergence of form by replication”, Proc.Natl.Acad. Sci.USA 94 (1997) 5024–5027.
Zinner, B., “Existence of traveling wavefront solutions for the discrete Nagumo equation”, SIAM J. Diff. Eqs. 96 (1992) 1–27.
Zinner, B., “Stability of traveling wavefronts for the discrete Nagumo equation”, SIAM J. Math. Anal. 22 (1991) 1016–1020.
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Nekorkin, V.I., Velarde, M.G. (2002). Mutual Synchronization, Control and Replication of Patterns and Waves in Coupled Lattices Composed of Bistable Units. In: Synergetic Phenomena in Active Lattices. Springer Series in Synergetics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56053-8_6
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DOI: https://doi.org/10.1007/978-3-642-56053-8_6
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