A one-dimensional nonlinear mapping is proposed that describes the dynamics of a passionary oscillator and is capable of transitioning to chaos through a series of period doubling bifurcations. Its dynamic behavior was studied and a bifurcation tree was constructed, which differs from the Feigenbaum diagram. Based on the formula of the passionary oscillator, a continuum cellular automaton has been developed, generating non-repeating symmetroids and quasi-chaotic distinctive structures. The system of passionary oscillators is considered as a possible basis for subsequent modeling of sociodynamic processes.

synergetics, passionarity, chaos, cellular automata, symmetroids, one-dimensional nonlinear mappings, oscillators, waves, science art

Kolesnikov Andrey Vitalievich,  ,  orcid.org/0000-0002-7620-0864,  Institute of Philosophy of the National Academy of Sciences of Belarus