Mapping nonlinear lattice equations onto cellular neural networks
Paul, S.; Huper, K.; Nossek, J.A.; Chua, L.O.
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
Volume 40, Issue 3, Mar 1993 Page(s):196 - 203
Digital Object Identifier 10.1109/81.222800
Summary:If one is only interested in the signals associated with
Hamiltonian systems, and not in conserving the energy in individual
circuit elements (nonlinear inductors and capacitors), then such systems
can be built as analog circuits, which implement some signal flow
graphs. Under certain restrictions, cellular neural networks (CNNs) come
very close to some Hamiltonian systems; therefore, they are potentially
useful for simulating or realizing such systems. It is shown how to map
two one-dimensional nonlinear lattices, the Fermi-Pasta-Ulam lattice and
the Toda lattice, onto a CNN. It is demonstrated for the Toda lattice
what happens if the signals are driven beyond the linear region of the
output function. Though the system is no longer Hamiltonian, numerical
experiments reveal the existence of solitons for special initial
conditions. This phenomenon is due to a special symmetry in the CNN
system of ordinary differential equations
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