Control of collective dynamics in a network of bistable time-delay systems coupled via the mean field

Background and Objectives: The object of our study is a network of identical bistable time-delayed feedback systems coupled via the mean field and driven by an external harmonic signal. The mean field that provides the global coupling of time-delay systems has its own delay time, which allows one to take into account the final speed of signal propagation and processing in the medium through which the oscillators are connected. The objective of the paper is to study the possibility of controlling the collective dynamics in the network of coupled bistable time-delay oscillators using an external harmonic force. Materials and Methods: The nonlinear function of oscillators and its parameters are chosen in such a way as to ensure the existence of bistable oscillatory regimes in which the basic frequencies of oscillations of the system differ by three times, with one of the bistable regimes being periodic and the other regime being chaotic. The initial conditions in the coupled oscillators are assigned in such a way that two clusters take place in the studied network, each of which, depending on the value of the phase shift of the mean field signal, can demonstrate both the synchronous and non-synchronous behavior of the elements included in it. The control of the oscillation regimes in the network is carried out using the variation of the parameters of the mean field and external harmonic signal. Results: It is shown that using a harmonic signal of relatively small amplitude, it is possible to effectively control the oscillation regimes, in particular, to create or destroy chimera states in a network of identical bistable systems with a time-delayed feedback that are globally coupled via the mean field.