Title :
Mapping nonlinear lattice equations onto cellular neural networks
Author :
Paul, S. ; Nossek, J.A. ; Chua, L.O.
Author_Institution :
Inst. for Network Theory & Circuit Design, Tech. Univ. Munich, Germany
Abstract :
The authors point out that because, under certain restrictions, cellular neural networks (CNNs) come very close to some Hamiltonian systems, they are potentially useful for simulating or realizing such systems. They show how to map two one-dimensional nonlinear lattices, the Fermi-Pasta-Ulam lattice (1965) and the Toda lattice (1975), onto a CNN. For the Toda lattice, they show what happens if the signals are driven beyond the linear region of the piecewise-linear output function. Though the system is no longer Hamiltonian, numerical experiments reveal the existence of soliton solutions for special initial conditions. This interesting phenomenon is due to a special symmetry in the CNN system of ordinary differential equations
Keywords :
neural nets; nonlinear equations; 1D nonlinear lattices; CNN; Fermi-Pasta-Ulam lattice; Toda lattice; cellular neural networks; nonlinear lattice equations; soliton solutions; special symmetry; Cellular neural networks; Circuit synthesis; Delay effects; Eigenvalues and eigenfunctions; Electrical engineering; Filtering; Lattices; Nonlinear equations; Solitons; Sorting;
Conference_Titel :
Cellular Neural Networks and their Applications, 1992. CNNA-92 Proceedings., Second International Workshop on
Conference_Location :
Munich
Print_ISBN :
0-7803-0875-1
DOI :
10.1109/CNNA.1992.274338