Abstract
An approach to solve the inverse problem of the reconstruction of the network of time-delay oscillators from their time series is proposed and studied in the case of the nonstationary connectivity matrix. Adaptive couplings have not been considered yet for this particular reconstruction problem. The problem of coupling identification is reduced to linear optimization of a specially constructed target function. This function is introduced taking into account the continuity of the nonlinear functions of oscillators and does not exploit the mean squared difference between the model and observed time series. The proposed approach allows us to minimize the number of estimated parameters and gives asymptotically unbiased estimates for a large class of nonlinear functions. The approach efficiency is demonstrated for the network composed of time-delayed feedback oscillators with a random architecture of constant and adaptive couplings in the absence of a priori knowledge about the connectivity structure and its evolution. The proposed technique extends the application area of the considered class of methods.
Highlights
Networks consisting of interacting oscillatory elements are extremely widespread in nature and technology
The topology of couplings plays an important role in the occurrence of a particular type of collective dynamics, while the dynamics of nodes and couplings affects the restructuring of the topology, i.e., there is a mutual interaction between the network dynamics and the evolution of network topology
To solve the ambitious task of reconstructing directed couplings in adaptive dynamical networks consisting of systems with an internal time delay, we propose an original approach based on a piece-wise linear interpolation of coupling dynamics in time, optimization of a specially constructed target function, and the separation of the recovered coupling coefficients into significant and insignificant coefficients
Summary
Networks consisting of interacting oscillatory elements are extremely widespread in nature and technology. The use of time-delay oscillators as network nodes brings the studied model systems closer to real objects of nature and human-created network structures. Oscillatory networks may have a complex architecture of connections between nodes and, along with network nodes, couplings between the nodes can have their own dynamics and exhibit evolution over time. Such adaptive dynamical networks, in which the topology of connections can be rearranged and the intensities of connections have their own dynamics, are widespread in the real world, for example, in neurodynamics and power supply networks [7,8,9,10,11]. The topology of couplings plays an important role in the occurrence of a particular type of collective dynamics, while the dynamics of nodes and couplings affects the restructuring of the topology, i.e., there is a mutual interaction between the network dynamics and the evolution of network topology
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