Hidden attractors in fundamental problems and engineering models

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered

Results on ββ\beta \beta β β decay with emission of two neutrinos or Majorons in 76^{76} 76 Ge from GERDA Phase I

A search for neutrinoless ββ decay processes accompanied with Majoron emission has been performed using data collected during Phase I of the GERmanium Detector Array (GERDA) experiment at the Laboratori Nazionali del Gran Sasso of INFN (Italy). Processes with spectral indices n = 1, 2, 3, 7 were searched for. No signals were found and lower limits of the order of 1023 yr on their half-lives were derived, yielding substantially improved results compared to previous experiments with 76Ge. A new result for the half-life of the neutrino-accompanied ββ decay of 76Ge with significantly reduced uncertainties is also given, resulting in (Formula presented.) yr