## National Academy of Sciences of Ukraine## Scientific Centre for Medical and Biotechnical Research## Laboratory of Mathematical Modeling of Nonlinear Processes15 Bogdana Khmelnytskogo Str, room 401 ## Submitted Papers:## Solitary states for coupled oscillators.Patrycja Jaros, Serhiy Brezetsky, Roman Levchenko, Dawid Dudkowski, Tomasz Kapitaniak, Yuri Maistrenko Chaotic Dynamics (nlin.CD); Dynamical Systems (math.DS), arXiv:1703.06950 ## We demonstrate that solitary states can be widely observed for networks of coupled oscillators with local, non-local and global couplings, and they preserve in both thermodynamic and Hamiltonian limits. We show that depending on units' and network's parameters, different types of solitary states occur, characterized by the number of isolated oscillators and the disposition in space. The creation of solitary states through the homoclinic bifurcation is described and the regions of co-existence of obtained states and typical examples of dynamics have been identified. Our analysis suggests that solitary states can be observed in a wide class of networks relevant to various real-world systems.## Multiple scroll wave chimera states.Volodymyr Maistrenko, Oleksandr Sudakov, Oleksiy Osiv and Yuri Maistrenko The European Physical Journal Special Topics, reference epjst170007, arXiv:1702.00161 ## We refer the appearance of three-dimensional (3D) multiheaded chimera states that display cascades of self-organized spatiotemporal patterns of coexisting coherence and incoherence. We demonstrate that number of the incoherent chimera’s domains can grow additively under appropriate varying the system parameters generating thereby head-adding cascades of the scroll wave chimeras. The phenomenon is derived for Kuramoto model of N identical phase oscillators placed in the 3D cube with periodic boundary conditions, parameters are coupling radius r and phase lag α. To obtain the multiheaded chimeras, we perform the so-called ’cloning procedure’ as follows: choose a sample single-headed 3D chimera state, make appropriate scale transformation, and put some number of copies of them into the unit cube. After, start numerical simulations with slightly perturbed initial conditions for long enough time to confirms or denies the state existence and stability. It is found, by this a way, that multiple scroll wave chimeras including those with incoherent rolls, Hopf links and trefoils admit this sort of multiheaded regeneration. On the other hand, multiple 3D chimeras without spiral rotations, like coherent and incoherent balls, tubes, crosses, and layers appear to be unstable under are destroyed rather fast even with any small perturbations.## Recent Publications:## Smallest chimera states.Yuri Maistrenko, Serhiy Brezetsky, Patrycja Jaros, Roman Levchenko and Tomasz Kapitaniak. PHYSICAL REVIEW E 95, 010203(R) (2017). doi: 10.1103/PhysRevE.95.010203. We demonstrate that chimera behavior can be observed in small networks consisting of three identical ## The smallest chimera state for coupled pendula.Wojewoda J, Czolczynski K, Maistrenko Y, Kapitaniak T. Sci Rep. 2016 Oct 7;6:34329. doi: 10.1038/srep34329. |