Yoshiki Sugitani

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.

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.

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.

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.