An equivalent electrical circuit for the Hindmarsh‐Rose model

Abstract

Summary Hardware realizations of neural networks can pave the way towards a new generation of processors due to the biological role model being superior in terms of speed and energy‐efficiency compared to today's processors. This can be achieved by deriving novel design principles for circuits being obtainable when replicating and investigating real biological neural networks in depth. This has, for example, been done by utilizing the Hindmarsh‐Rose model, offering a rich repertoire of neuronal firing patterns. Our aim is to synthesize a theoretical, equivalent electrical circuit of the Hindmarsh‐Rose model being well interpretable in terms of biology, since this supports the derivation of design principles from biology and can serve as a basis for a systematic circuit simplification. We do this by starting from a linearized model because this allows for a systematic approach and then first derive a linear and afterwards a nonlinear equivalent electrical circuit. The resulting circuit has a structure similar to conductance‐based models, where a deployed negative impedance converter can be seen as a deeper modeling of ion pump activity. Simulation results of the proposed circuits show the functionality of the equivalent circuits.

Oscillator networks with N‐shaped nonlinearities: Electrical modeling and wave digital emulation

“…These destabilize the equilibrium point of the system while semi‐passivity guarantees bounded trajectories, leading to oscillations 10,11 . For example, the relaxation oscillator, 12 the Hindmarsh‐Rose oscillator, 13 the FitzHugh‐Nagumo oscillator (FNO), 14 or the classical differential LC oscillator 15 the locally active component takes the form of an N‐shaped nonlinearity. The name of these one‐ports stems from their $$$ \left(i,u\right) $$$ curve which assumes the shape of the letter “N”.…”

Bio-inspired augmented reality: an interactive, digital twin ofC. elegans

“…The concept of a digital twin of C. elegans that can emulate locomotion behavior has also been explored in [14] by means of a very different approach based on using machine learning and an offline dataset to train a neural network consisting of 469 nodes and including 4869 chemical connections and 1433 electrical connections. Instead, we describe each neuron via the Hindmarsh-Rose model and propose a model for neuron behavior based on the equivalent electrical circuit from [15] and a locomotion model based on [16].…”

“…The proposed model of C. elegans can be realized directly as an electronic circuit [15] and is additionally implemented as a simulation in software. The advantages of simulating the electrical circuit with the wave digital concept are efficiency, modularity, numerical stability, real-time processing capabilities, potential for low computational complexity in certain applications, and ultimately a deeper understanding of the circuits as a didactic advantage.…”