Control of collective dynamics in multiplex networks of bistable time-delayed feedback oscillators with switched couplings

Abstract

Background and Objectives: The study of complex collective dynamics in networks of coupled oscillators and its control is an important task for many scientific disciplines. Networks of nonlinear oscillators are capable of demonstrating a wide variety of spatiotemporal regimes of collective dynamics. One of these regimes is a chimera state that occurs in networks of identical oscillators and is characterized by the simultaneous existence in the network of both oscillators performing synchronous oscillations and oscillators with asynchronous behavior. The object of study in this paper is chimera states in multiplex networks consisting of three coupled rings, each of which consists of coupled identical bistable time-delay oscillators. Materials and Methods: The cases of unidirectional and mutual, time-varying couplings between rings (layers) of the network are considered. The control of collective dynamics, including chimera states in three-layer networks, was carried out by us in a radio physical experiment, in which radio engineering generators with time-delayed feedback were used as the node elements of the network. Each generator was a ring system consisting of a delay line, a nonlinear element, and a first-order low-frequency RC-filter. To implement the couplings between the network generators, an approach was used in which the couplings in the experimental setup are set programmatically. The control of chimera states in the network is implemented by an appropriate choice of initial conditions for bistable generators and by changing the topology of couplings between network layers. Results: It has been shown that at strong unidirectional coupling between the layers of the network, the chimera state is copied from layer to layer due to the synchronization of driven generators. At bidirectional coupling between the layers of the network, one can observe both the phenomenon of cloning of chimera states and the destruction of chimera states, depending on the choice of initial conditions for bistable generators. Conclusion: The obtained results are useful for better understanding the mechanisms of emergence of complex regimes of collective dynamics in multiplex networks with switched couplings.

Keywords

• multiplex networks
• adaptive couplings
• bistable oscillators
• time-delay generators
• chimera states