Elementary particles possess quantized values of charge and internal angular momentum or spin. These characteristics do not change when the particles interact with other particles or fields as long as they preserve their entities. Quantum theory does not explain this quantization. It is introduced into the theory a priori. An interacting particle is an open system and thus does not obey conservation laws. However, an open system may create dynamically stable states with unchanged dynamical variables via self-organization. In self-organized systems stability is achieved through the interplay of nonlinearity and dissipation. Can self-organization be responsible for particle formation? In this paper we develop and analyze a particle model based on qualitative dynamics and the Feigenbaum universality. This model demonstrates that elementary particles can be described as self-organized dynamical systems belonging to a wide class of systems characterized by a hierarchy of period-doubling bifurcations. This semi-qualitative heuristic model gives possible explanations for charge and action quantization, and the origination and interrelation between the strong, weak, and electromagnetic forces, as well as SU(2) symmetry. It also provides a basis for particle taxonomy endorsed by the Standard Model. The key result is the discovery that the Planck constant is intimately related to elementary charge.
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