Reservoir computing with state-dependent time delay

We examine a new design of reservoir computing based on an otherwise linear dynamical system subject to feedback in which a delay time linearly depends on the system's state. Despite the apparent linearity of the system under casual perusal, the system nonetheless possesses a nonlinearity that can be used for time-delay reservoir computing. We find that close multiple Hopf bifurcation points lead to a rich sawtooth-shaped transient response to input signals, which can be beneficial for computing capabilities. We benchmark the reservoir computing system's memory capacity and performance on solving delayed XOR, Iris flower classification tasks, and the Santa Fe time-series prediction task. We demonstrate how the nonlinearity and the memory capacity of the system can be tuned by changing the time-delay dependence.