We describe and discuss the similarites in two different kinds of physical systems: Chua's circuit (and, broady speaking, chaotic systems) and atoms in the Periodic Table. We anayze the regularities arising from the chaotic nature of the former against the regularities in the energy spectra of the second. We show the existing analogies among the Bohr's law and the bifurcation diagram building a map connecting each energy level in atoms to each point in the bifurcation diagram in the parameter space. We found a genera rule valid for many element of the Periodic Table by calculating the two-dimensional bifurcation diagram versus Bohr's law. The result is a one-to-one correspondence between atoms and nonlinear Chua's circuits. Finaly we discuss possible implications of the model when applied to more complicated systems like molecules or atomic clusters.