Abstract
This study firstly presents (i) a novel general cellular mapping scheme for two dimensional neuromorphic dynamical systems such as bio-inspired neuron models, and (ii) an efficient mixed analog-digital circuit, which can be conveniently implemented on a hybrid memristor-crossbar/CMOS platform, for hardware implementation of the scheme. This approach employs 4n memristors and no switch for implementing an n-cell system in comparison with 2n2 memristors and 2n switches of a Cellular Memristive Dynamical System (CMDS). Moreover, this approach allows for dynamical variables with both analog and one-hot digital values opening a wide range of choices for interconnections and networking schemes. Dynamical response analyses show that this circuit exhibits various responses based on the underlying bifurcation scenarios which determine the main characteristics of the neuromorphic dynamical systems. Due to high programmability of the circuit, it can be applied to a variety of learning systems, real-time applications, and analytically indescribable dynamical systems. We simulate the FitzHugh-Nagumo (FHN), Adaptive Exponential (AdEx) integrate and fire, and Izhikevich neuron models on our platform, and investigate the dynamical behaviors of these circuits as case studies. Moreover, error analysis shows that our approach is suitably accurate. We also develop a simple hardware prototype for experimental demonstration of our approach.
Highlights
The human nervous system is an intriguing complex system capable of performing intricate tasks using an enormous number of neurons each connected via synapses to several thousand neighboring neurons
Note that our approach supports all four different abovementioned forms, but considering this fact that most of the popular neuron models such as the FitzHugh-Nagumo (Fitzhugh, 1961), Izhikevich (Izhikevich, 2003), and Adaptive Exponential (AdEx) (Brette and Gerstner, 2005) neural models, fit into the first simplified general form represented in Equation (2), we continue the rest of the paper based on this general form
At the moment when negative pulse is finished, anodal break is occurred, stable equilibrium point promptly shifts up, and the state point makes a transitory largeamplitude excursion to move from previous location of the stable point to its current location and rest. This transient state results in a single spike in time domain. This response is investigated on the FHN-Memristive Dynamical System (MDS) circuit in Figure 3C, and the results show that the approach can accurately produce this behavior
Summary
The human nervous system is an intriguing complex system capable of performing intricate tasks using an enormous number of neurons each connected via synapses to several thousand neighboring neurons. Our approach is a cellular-based system that discretizes dynamical variables resulting in a cellular phase plane, stores the equilibrium curves in a memristive crossbar-based analog memory block, evaluates the velocity and direction of the vector field in the cells, and tracks the state point in the space using VCOs and pointer registers This system is a fully reconfigurable general approach capable of implementing a wide range of two dimensional neuromorphic dynamical systems such as FitzHugh-Nagumo (FHN; Fitzhugh, 1961), Adaptive Exponential (AdEx) integrate and fire (Brette and Gerstner, 2005), and Izhikevich neuron models (Izhikevich, 2003).
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