CHAOTIC BEHAVIOR IN NONLINEAR LATTICES

Forced vibrations of nonlinear lattices, consisting of one or two particles vibrating one dimensionally, are investigated. Harmonic response, bifurcations and chaotic behaviour are considered. We use the Toda potential, the Morse potential and a third ''combined'' potential as the interaction potentials between the adjacent particles in the models. The third potential is obtained via a parametric combination of the Toda and Morse potentials. External loading is harmonic. The attractors, their phase portraits, the associated Lyapunov exponents and the power spectra are obtained and discussed. For different sets of parameters considered, the lattice shows periodic, quasi-periodic or chaotic character. The effect of the type of the interaction potential on the behaviour of the lattice is studied. Comparative results are presented in the form of attractor grids.