We study the synchronization behavior of a class of identical FitzHugh-Nagumo-type oscillators under adaptive coupling. We describe the oscillators by a circuit model and we provide a sufficient synchronization condition that relies on the shape of the nonlinear conductance’s $(i,u)$-curve and the connectivity of the adaptive coupling network. The coupling network is allowed to be time-variant, state-dependent and locally adaptive, where we treat memristive coupling elements as a special case. We provide a physical interpretation of synchronization in terms of power dissipation and investigate the sharpness of our condition.

We report on a systematic procedure for the port-wise decomposition of electrical networks, which we refer to as the template-based approach. Our method exploits the SPQR-tree decomposition as an algorithmic procedure for decomposing a given circuit into a maximal set of one- and multiports. In particular, we provide a solution for representing subcircuits by suitable template graphs, such that they are encapsulated not decomposed/processed by the SPQR-algorithm. Contrary to current methods, our replacement graphs are not sophisticated but rather simple, which, in general, enhances the performance of the algorithm, when it comes to decomposing large electrical networks with multiports. Some electrical devices, such as transistors or op-amps, are commonly described in terms of their terminals rather than their ports. Thus, we cover the application of the template-based approach to three-terminal devices. Lastly, we discuss the advantages of the template-based SPQR-tree decomposition in the context of wave digital emulation.

We study the synchronization behavior of a class of identical FitzHugh-Nagumo-type oscillators under linear diffusive coupling. We describe the oscillators by a circuit model and we provide a sufficient synchronization condition that relies on the shape of the nonlinear conductance’s (i, u)-curve and the connectivity of the linear coupling network. We propose that this condition may have benefits with regard to the design of neuromorphic circuits using such oscillators and furthermore investigate how sharp our condition is.

The reliable and compact modeling of RRAM devices is crucial for supporting the development of novel technologies including them. The latter includes a wide range of applications, such as in-memory computing in neuromorphic networks or memristive logic. A major advantage of the considered HfO2- based RRAM devices is their CMOS-compatibility, which allows them to already be utilized in present applications. However, one problem with RRAMs is that their fabrication still leads to device variabilities. This makes it challenging to test the functionality of aspiring technologies utilizing them in an experimental fashion. This work is dedicated to the compact modeling and efficient emulation of 1T-1R RRAM devices. Specifically, we aim to provide an enhanced model, based on the Stanford-PKU model, that can be used on any simulation platform such as SPICE, VERLIOGA, or even standard ODE solvers to simulate multilevel capable RRAM devices. Furthermore, we provide an algorithmic model, based on the wave digital concept, which allows for emulating the considered RRAM device in real-time. Using the latter, we show the hysteresis of our enhanced model to exhibit astounding resemblance with real device measurements.

The standard van Neumann computer excels at many things. However, it can be very inefficient in solving optimization problems with a large solution space. For that reason, a novel analog approach, the oscillator-based Ising machine, has been proposed as a better alternative for dealing with such problems. In this work, we review the concept of oscillator-based Ising machines. In particular, we address how optimization problems can be mapped onto such machines when the QUBO formulation is given. Furthermore, we provide an ideal circuit that can be used in combination with the wave digital concept for real-time simulated annealing. The functionality of this circuit is explained on the basis of a Lyapunov stability analysis. The latter also provides an answer for the question: when has the Ising machine solved a mapped problem? At the end, we provide emulation results demonstrating the correlation between functionality and stability of the discussed machine. These results show that mapping a problem onto an Ising machine effectively maps the solution of the problem onto an equilibrium of the phase space.