Here, applying the Scale-Symmetric Theory (SST), we show how particle physics via the Chaos Theory leads to the cosmological dark-matter structures and mental solitons. Moreover, the interactions of the cosmological dark-matter structures with baryonic matter via weak interactions of leptons, lead to the untypical motions of stars in galaxies and to other cosmological structures such as AGN composed of a torus and a central-condensate/modified-black-hole or solar system. Most important in the Chaos Theory (ChT) is to understand physical meaning of a logistic map for the baryons - it concerns the black-body spectrum and the ratio of the masses of charged kaon and pion. Such logistic map leads to the first Feigenbaum constant related to the period-doubling bifurcations that in a limit lead to the onset of chaos. In the period-doubling bifurcations for proton there appear the orbits of period-4 and higher periods. We show that the orbits of period-4 follow from the structure of baryons and that they lead to the Titius-Bode law for the nuclear strong interactions. Calculated here on base of the structure of proton the first Feigenbaum constant is 4.6692033 and it is close to the mathematical value 4.6692016…