Anharmonicity, neural-like lattices, and fast signal/electric transmission

Anharmonic interactions in lattices may sustain robust oscillatory modes and (nonlinear) waves including solitons. This is illustrated here by using an exponentially repulsive interaction introduced by Toda. To cope with friction and dissipation -always present in real systemsand hence to make robust, e.g., solitons, following Lord Rayleigh, an appropriate input-output energy balance is added to the dynamics. Noise (and hence temperature) is also incorporated by embedding the system in a Gaussian, white noise environment (thermal bath). In the particular case of a lattice ring with six units it is shown how such a Toda-Rayleigh lattice can be used as a Central Pattern Generator of three different oscillatory modes. These three modes are shown to map three walking (metachronal/low speed, caterpillar/medium speed, and tripod/fast speed) gaits in insects (hexapods). An electronic implementation (diodes map easily exponential interactions) of the TodaRayleigh lattice ring is also discussed, including leg motor controls for an hexapod robot. Finally, the Toda-Rayleigh mechanical lattice is converted into an electromechanical wire-like, lattice electric conductor. This is done by considering the lattice units as positive ion cores and adding free electrons to the system. The coupling of Toda dynamics with Coulomb interactions yields remarkable currentfield/voltage and current-temperature characteristics in the presence of an external electric field. An Ohmic-non Ohmic transition is possible in the lattice conductor. Such feature permits to consider it as a neural-like conveyor of subsonic (Ohmic) and fast supersonic (non-Ohmic) electric or other signals.