Охота на химер в полносвязных сетях нелинейных осцилляторов

Известия высших учебных заведений. Прикладная нелинейная динамика. 2022. Т. 30. № 2. С. 152–175.

Glyzin D., Глызин С. Д., Колесов А. Ю.

The purpose of this work is to study the dynamic properties of solutions of special systems of ordinary
differential equations, called fully connected networks of nonlinear oscillators. Methods. A new approach to obtain
periodic regimes of the chimeric type in these systems is proposed, the essence of which is as follows. First, in the
case of a symmetric network, a simpler problem is solved of the existence and stability of quasi-chimeric solutions —
periodic regimes of two-cluster synchronization. For each of these modes, the set of oscillators falls into two disjoint
classes. Within these classes, full synchronization of oscillations is observed, and every two oscillators from different
classes oscillate asynchronously. Results. On the basis of the proposed methods, it is separately established that in
the transition from a symmetric system to a general network, the periodic regimes of two-cluster synchronization
can be transformed into chimeras. Conclusion. The main statements of the work concerning the emergence of
chimeras were obtained analytically on the basis of an asymptotic study of a model example. For this example,
the notion of a canonical chimera is introduced and the statement about the existence and stability of solutions
of chimeric type in the case of asymmetry of the network is proved. All the results presented are extended to a
continuous analogue of the corresponding system. The obtained results are illustrated numerically.

Keywords: устойчивость, буферность, полносвязная сеть нелинейных осцилляторов