Delay-induced amplitude death in multiplex oscillator network with frequency-mismatched layers.

The present paper analytically investigates the stability of amplitude death in a multiplex Stuart-Landau oscillator network with a delayed interlayer connection. The network consists of two frequency-mismatched layers, and all oscillators in each layer have identical frequencies. We show that, if the matrices describing the network topologies of each layer commute, then the characteristic equation governing the stability can be reduced to a simple form. This form reveals that the stability of amplitude death in the multiplex network is equally or more conservative than that in a pair of frequency-mismatched oscillators coupled by a delayed connection. In addition, we provide a procedure for designing the delayed interlayer connection such that amplitude death is stable for any commuting matrices and for any intralayer coupling strength. These analytical results are verified through numerical examples. Moreover, we numerically discuss the results for the case in which the commutative property does not hold.

Amplitude death in delay-coupled oscillators on directed graphs.

The present paper investigates amplitude death (AD) in delay-coupled oscillators on directed graphs, in which the connection delays among oscillators are heterogeneous. We reveal that a linear stability analysis of AD can be significantly simplified by focusing on directed cycles in the graph. First, it is proven that the characteristic function of a steady state can be factorized into several functions that can be analyzed independently. Second, we show that the number of connection parameters to be considered for the stability analysis can be reduced, because the stability depends on the sums of connection delays for directed cycles and is independent of the connection delays on edges that do not form directed cycles. The theoretical results are verified through numerical simulations.

Effects of frequency mismatch on amplitude death in delay-coupled oscillators.

The present paper analytically reveals the effects of frequency mismatch on the stability of an equilibrium point within a pair of Stuart-Landau oscillators coupled by a delay connection. By analyzing the roots of the characteristic function governing the stability, we find that there exist four types of boundary curves of stability in a coupling parameters space. These four types depend only on the frequency mismatch. The analytical results allow us to design coupling parameters and frequency mismatch such that the equilibrium point is locally stable. We show that, if we choose appropriate frequency mismatches and delay times, then it is possible to induce amplitude death with strong stability, even by weak coupling. In addition, we show that parts of these analytical results are valid for oscillator networks with complete bipartite topologies.

Synchronizing Chaos with Imperfections.

Previous research on nonlinear oscillator networks has shown that chaos synchronization is attainable for identical oscillators but deteriorates in the presence of parameter mismatches. Here, we identify regimes for which the opposite occurs and show that oscillator heterogeneity can synchronize chaos for conditions under which identical oscillators cannot. This effect is not limited to small mismatches and is observed for random oscillator heterogeneity on both homogeneous and heterogeneous network structures. The results are demonstrated experimentally using networks of Chua's oscillators and are further supported by numerical simulations and theoretical analysis. In particular, we propose a general mechanism based on heterogeneity-induced mode mixing that provides insights into the observed phenomenon. Since individual differences are ubiquitous and often unavoidable in real systems, it follows that such imperfections can be an unexpected source of synchronization stability.

Artificial intelligence supported anemia control system (AISACS) to prevent anemia in maintenance hemodialysis patients.

Anemia, for which erythropoiesis-stimulating agents (ESAs) and iron supplements (ISs) are used as preventive measures, presents important difficulties for hemodialysis patients. Nevertheless, the number of physicians able to manage such medications appropriately is not keeping pace with the rapid increase of hemodialysis patients. Moreover, the high cost of ESAs imposes heavy burdens on medical insurance systems. An artificial-intelligence-supported anemia control system (AISACS) trained using administration direction data from experienced physicians has been developed by the authors. For the system, appropriate data selection and rectification techniques play important roles. Decision making related to ESAs poses a multi-class classification problem for which a two-step classification technique is introduced. Several validations have demonstrated that AISACS exhibits high performance with correct classification rates of 72%-87% and clinically appropriate classification rates of 92%-98%.

Amplitude suppression of oscillators with delay connections and slow switching topology.

The present paper shows that the amplitudes of oscillators in delay-coupled oscillator networks can be suppressed by switching the network topology at a rate much lower than the oscillator frequencies. The mechanism of suppression was clarified numerically, and a procedure for determining the connection parameters to induce suppression is presented. The analytical and numerical results were obtained with Stuart-Landau oscillators and were experimentally validated using double-scroll chaotic circuits.

Design of coupling parameters for inducing amplitude death in Cartesian product networks of delayed coupled oscillators.

The present study investigates amplitude death in Cartesian product networks of two subnetworks, where each subnetwork has a different coupling delay. The property of the Cartesian product helps us to analyze the stability of amplitude death. Our analysis reveals that amplitude death can occur for long coupling delays if there is a suitable difference in the coupling delays in the two subnetworks. Furthermore, based on the edge theorem in robust control theory, we propose two design procedures of coupling parameters for inducing amplitude death in the Cartesian product networks. Our procedures do not require any information of topologies of the subnetworks. The validity of these procedures is numerically confirmed.

Dynamical behavior and peak power reduction in a pair of energy storage oscillators coupled by delayed power price.

This paper investigates dynamics of a management system for controlling a pair of energy storages. The system involves the following two characteristics: each storage behaves in a manner that reduces the number of charge noncharge cycles and begins to be charged when the price of power is lower than a particular price threshold. The price is proportional to the past total power flow from a power grid to all storages. A peak of the total power flow occurs when these storages are charged simultaneously. From the viewpoint of nonlinear dynamics, the energy storages can be considered as relaxation oscillators coupled by a delay connection. Our analytical results suggest that the peak can be reduced by inducing an antiphase synchronization in coupled oscillators. We confirm these analytical results through numerical simulations. In addition, we numerically investigate the dynamical behavior in 10 storages and find that time delay in the connection is important in reducing the peak.

Delay- and topology-independent design for inducing amplitude death on networks with time-varying delay connections.

We present a procedure to systematically design the connection parameters that will induce amplitude death in oscillator networks with time-varying delay connections. The parameters designed by the procedure are valid in oscillator networks with any network topology and with any connection delay. The validity of the design procedure is confirmed by numerical simulation. We also consider a partial time-varying delay connection, which has both time-invariant and time-varying delays. The effectiveness of the partial connection is shown theoretically and numerically.

Dynamics of dc bus networks and their stabilization by decentralized delayed feedback.

The present paper deals with the dynamics of bus networks, which consist of several identical dc bus systems connected by resistors. It is analytically guaranteed that the stability of a stand-alone dc bus system is equivalent to that of the networks, independent of the number of bus systems and the network topology. In addition, we show that a decentralized delayed-feedback control can stabilize an unstable operating point embedded within the networks. Moreover, this stabilization does not depend on the number of bus systems or the network topology. A systematic procedure for designing the controller is presented. Finally, the validity of the analytical results is confirmed through numerical examples.

Analysis of a dc bus system with a nonlinear constant power load and its delayed feedback control.

This paper tackles a destabilizing problem of a direct-current (dc) bus system with constant power loads, which can be considered a fundamental problem of dc power grid networks. The present paper clarifies scenarios of the destabilization and applies the well-known delayed-feedback control to the stabilization of the destabilized bus system on the basis of nonlinear science. Further, we propose a systematic procedure for designing the delayed feedback controller. This controller can converge the bus voltage exactly on an unstable operating point without accurate information and can track it using tiny control energy even when a system parameter, such as the power consumption of the load, is slowly varied. These features demonstrate that delayed feedback control can be considered a strong candidate for solving the destabilizing problem.

Design of time-delayed connection parameters for inducing amplitude death in high-dimensional oscillator networks.

The present paper studies time-delayed-connection induced amplitude death in high-dimensional oscillator networks. We provide two procedures for design of a coupling strength and a transmission delay: these procedures do not depend on the topology of oscillator networks (i.e., network structure and number of oscillators). A graphical procedure based on the Nyquist criterion is proposed and then is numerically confirmed for the case of five-dimensional oscillators, called generalized Rössler oscillators, which have two pairs of complex conjugate unstable roots. In addition, for the case of high-dimensional oscillators having two unstable roots, the procedure can be systematically carried out using only a simple algebraic calculation. This systematic procedure is numerically confirmed for the case of three-dimensional oscillators, called Moore-Spiegel oscillators, which have two positive real unstable roots.