Objectives. Recently studied phenomena in condensed matter physics have prompted new insights into the dynamic theory of crystals. The results of numerous experimental data demonstrate the impossibility of their explanation within the framework of linear models of the dynamics of many-particle systems, resulting in the necessity to account for nonlinear effects. Analyzing the dynamics of systems in condensed matter physics containing a sufficiently large number of particles shows that modes of motion can undergo changes depending on the potential of interparticle interaction. This is also reflected in the presence of domains with essentially chaotic phase space having a number of degrees of freedom N ≥ 1.5 and a certain set of interparticle interaction parameters. However, it is not only the dynamic model that appears to be strongly nonlinear. A similar nature of motion can be also observed in a static nonlinear many-particle system. The paper aims to study the influence of the external field specified by the interatomic triple-well potential on the equilibrium structure of a chain of interacting atoms.Methods. Methods of Hamiltonian mechanics are used.Results. Analytical expressions are obtained and analyzed for determining the phase portrait of the equilibrium structure of a chain of interacting atoms for various values of the parameter characterizing the local potential of the field in which each atom of the chain moves. Phase portraits of the equilibrium structure of the system are constructed in continuous and discrete representations of the equilibrium equations for various values of the parameter characterizing the local potential of the field in which each atom of the chain moves.Conclusions. It is shown that both periodic and random chaotic arrangements of atoms are implemented depending on the magnitude of the external field.
