This work deals with bifurcation and the chaotic behavior in one dimensional chains of small particles. We consider two distinct possibilities, one where the particles are modeled by a fourth-order potential which was already studied. We revisit this system and bring novelties concerning the presence of the three-armed star behavior and the study of the corresponding Lyapunov exponent. The other system is new, and there the particles are more involved and modeled by an eighth-order potential. We investigate this new system within the same approach, emphasizing the behavior of the orbits, the bifurcation profile and the corresponding Lyapunov exponent.
Categories: nlin.CD math-ph math.MP