Duffing oscillator, cases of symmetry breaking

Author: Tamar Nikvashvili
Co-authors: Tamar Nikvashvili
Keywords: Symmetry, nonlinearity, duffing oscillator.
Annotation:

Many systems in nature have stable states separated by energy barriers, when the system has the ability to "move" between stable states, in this case the dynamics are very complex. The discussed issue is, in fact, a generalized task, it can be mentioned in many fields: in quantum mechanics, field theory, hydrodynamics, wherever the movement of particles in a solid body takes place in a potential environment, that is, the potential energy of the environment is created by the surrounding bodies. The action can be electrical, gravitational, magnetic... this logic applies everywhere. In this model, the function corresponding to the potential energy has a dual structure. The system is tested with different effects, the corresponding spatial trajectories are obtained. It is investigated in a non-dissipative way, and then the damping components are also included in the system. The system seems to simultaneously lose energy and at the same time gain it under the influence of an external force. At this time, the result is so chaotic that it is impossible to "predict" anything.