Odd and even intrinsic modes in diatomic nonlinear lattices

Systematic simulations of a one-dimensional diatomic dynamical lattice with cubic and quartic anharmonicity demonstrate that the odd (Sievers-Takeno) intrinsic mode is stable at relatively low frequencies, being changed by the even (Page) one at some critical frequency. The transition between the two modes is hysteretic, i.e., it depends upon the direction of change of the frequency. The critical frequency is a growing function of the mass difference between the particles with the odd and even numbers, but it proves to be practically independent of the ratio between the quadratic and cubic terms in the equations of motion.