  We have proposed a simple one-dimensional model of internal particle
dynamics. The model is based on the assumption that self-interaction can be
represented by a nonlinear feedback and described by a quadratic recurrent map.
Charge plays the role of a generalized dynamical variable and a feedback
coupling parameter. The model suggests that charge and action quantization stem
from the system's dissipative quality and from a hierarchy of supercycle orbits
located between period-doubling bifurcations on the Feigenbaum tree. Among the
numerical results, we have discovered a link between the quantum of action and
the elementary charge. We also found that the fine structure constant can with
a good accuracy be expressed exclusively through mathematical constants,
including the Feigenbaum delta. We have introduced dimensionless numbers that
describe the relative role of the internal particle dynamics when both internal
and external dynamics are taken into consideration. We have found these numbers
to be close to the electron, proton, and neutron g-factors known from the
experiment.
