Methods of nonlinear dynamics and equilibrium structures of magnetoelastic chains

Disorder of particle chains as a dynamical problem of transition to chaos: Analogy to simulation induced chaos

“…1. The particle chain equilibria problem gives us a good example of the efficiency of dynamical methods; see [2]- [5] and [8]. In general, the idea of applying dynamical methods can be formulated as the problem of solving a set of equilibria equations V. V. BELOSHAPKIN, A. G .…”

“…(1) to (3) one has (4) where (5) and prime means the derivative with respect to the argument. Using definition ( 5 ) and a new variable 91)+1 = 9; + V ' ( X j ) 9 j = 9 ( X jx j -1 ) (6) P j = x jx j -1 it follows from (4H6) that (7) where we assume that 9' # 0 nowhere in the domain of consideration.…”