title: Imperfect chimera states for coupled pendula.
abstract: The phenomenon of chimera states in the systems of coupled, identical oscillators has attracted a great deal of recent theoretical and experimental interest. In such a state, different groups of oscillators can exhibit coexisting synchronous and incoherent behaviors despite homogeneous coupling. Here, considering the coupled pendula, we find another pattern, the so-called imperfect chimera state, which is characterized by a certain number of oscillators which escape from the synchronized chimera's cluster or behave differently than most of uncorrelated pendula. The escaped elements oscillate with different average frequencies (Poincare rotation number). We show that imperfect chimera can be realized in simple experiments with mechanical oscillators, namely Huygens clock. The mathematical model of our experiment shows that the observed chimera states are controlled by elementary dynamical equations derived from Newton's laws that are ubiquitous in many physical and engineering systems.
authors.affiliation: Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland.
authors.forename: Tomasz
authors.initials: T
authors.lastname: Kapitaniak
authors.affiliation: Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland.
authors.forename: Patrycja
authors.initials: P
authors.lastname: Kuzma
authors.affiliation: Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland.
authors.forename: Jerzy
authors.initials: J
authors.lastname: Wojewoda
authors.affiliation: Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland.
authors.forename: Krzysztof
authors.initials: K
authors.lastname: Czolczynski
authors.affiliation: 1] Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland [2] Institute of Mathematics and Centre for Medical and Biotechnical Reserch, National Academy of Sciences of Ukraine, Tereshchenkivska st. 3, 01030 Kyiv, Ukraine.
authors.forename: Yuri
authors.initials: Y
authors.lastname: Maistrenko