CMOS circuit implementations for neuron models

The mathematical neuron basic cells used as basic cells in popular neural network architectures and algorithms are discussed. The most popular neuron models (without training) used in neural network architectures and algorithms (NNA) are considered, focusing on hardware implementation of neuron models used in NAA, and in emulation of biological systems. Mathematical descriptions and block diagram representations are utilized in an independent approach. Nonoscillatory and oscillatory models are discusse

Stability Analysis of FitzHugh-Nagumo with Smooth Periodic Forcing

Alan Lloyd Hodgkin and Andrew Huxley received the 1963 Nobel Prize in Physiology for their work describing the propagation of action potentials in the squid giant axon. Major analysis of their system of differential equations was performed by Richard FitzHugh, and later by Jin-Ichi Nagumo who created a tunnel diode circuit based upon FitzHugh’s work. The resulting differential model, known as the FitzHugh-Nagumo (FH-N) oscillator, represents a simplification of the Hodgkin-Huxley (H-H) model, but still replicates the original neuronal dynamics (Izhikevich, 2010). We begin by providing a thorough grounding in the physiology behind the equations, then continue by introducing some of the results established by Kostova et al. for FH-N without forcing (Kostova et al., 2004). Finally, this sets up our own exploration into stimulating the system with smooth periodic forcing. Subsequent quantification of the chaotic phase portraits using a Lyapunov exponent are discussed, as well as the relevance of these results to electrocardiography

Stability Analysis of FitzHugh–Nagumo with Smooth Periodic Forcing

Alan Lloyd Hodgkin and Andrew Huxley received the 1963 Nobel Prize in Physiology for their work describing the propogation of action potentials in the squid giant axon. Major analysis of their system of differential equations was performed by Richard FitzHugh, and later on by Jin-ichi Nagumo who created a tunnel diode circuit based upon FitzHugh\u27s work. The subsequent differential equation model, known as the FitzHugh-Nagumo (FH-N) oscillator, represents a simplification of the Hodgkin-Huxley (H-H) model, but still replicates the original neuronal dynamics. This thesis begins by providing a thorough grounding in the physiology behind the equations. We continue by proving some of the results postulated by Tanya Kostova et al. for FH-N without forcing. Finally, this sets up our own exploration into stimulating the system with smooth periodic forcing. Subsequent quantification of the chaotic phase portraits using a Lyapunov exponent are discussed, as well as the relevance of these results to electrocardiography

Embedding the dynamics of a single delay system into a feed-forward ring

We investigate the relation between the dynamics of a single oscillator with delayed self-feedback and a feed-forward ring of such oscillators, where each unit is coupled to its next neighbor in the same way as in the self-feedback case. We show that periodic solutions of the delayed oscillator give rise to families of rotating waves with different wave numbers in the corresponding ring. In particular, if for the single oscillator the periodic solution is resonant to the delay, it can be embedded into a ring with instantaneous couplings. We discover several cases where the stability of a periodic solution for the single unit can be related to the stability of the corresponding rotating wave in the ring. As a specific example we demonstrate how the complex bifurcation scenario of simultaneously emerging multi-jittering solutions can be transferred from a single oscillator with delayed pulse feedback to multi-jittering rotating waves in a sufficiently large ring of oscillators with instantaneous pulse coupling. Finally, we present an experimental realization of this dynamical phenomenon in a system of coupled electronic circuits of FitzHugh-Nagumo type

Hardware Coupled Nonliear Oscillators as a Model of Retina

An electronic circuit consisting of coupled nonlinear oscillators⁴＇⁵ simulates the spatiotemporal processing in retina. Complex behavior recorded in vivo from ganglion cells in the cat retina 6 in response to flickering light spots is matched by setting the coupling parameters in the hardware oscillators. An electronic neuron (c-neuron) is composed of four coupled oscillators: three representing the light driven generator potential of the ganglion cell, the other representing membrane spiking. A 1-D ring of e-neurons reflects the connectivity in the retina: strong neighborhood excitation, and wider inhibition. E-neurons, like retinal ganglion cells, exhibit spontaneous spiking. Driving more than one e-neuron with a sinusoidally modulated input increases regularity in the e-neurons responses, as is found in the retina. We encoded c-neuron activity into single-bit spike trains and found chaotic spontaneous oscillations using close return histograms. The model's behavior gives a new understanding of neurophysiological findings.Whitehall (S93-24); Air Force Office of Scientific Research (F49620-92-J-0499, F49620-92-J-0334); Office of Naval Research (N00014-89-J-1377, N00014-95-I-0409); MIT Undergraduate Research Oppurtunities Progra

Bursting through interconnection of excitable circuits

We outline the methodology for designing a bursting circuit with robustness and control properties reminiscent of those encountered in biological bursting neurons. We propose that this design question is tractable when addressed through the interconnection theory of two excitable circuits, realized solely with first-order filters and sigmoidal I-V elements. The circuit can be designed and controlled by shaping its I-V curves in the relevant timescales, giving a novel and intuitive methodology for implementing single neuron behaviors in hardware.The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet n.670645

BIFURCATION AND CHAOS IN COUPLED BVP OSCILLATORS

Bonhöffer-van der Pol(BVP) oscillator is one of classic model exhibiting typical nonlinear phenomena in the planar autonomous system. This paper gives an analysis of equilibria, periodic solutions, strange attractors of two BVP oscillators coupled by a resister. When an oscillator is fixed its parameter values in non-oscillatory region and the other is in oscillatory regin, then the double scroll attractor is emerged by the coupling. Bifurcation diagrams are obtained numerically from the mathematical model and chaotic parameter regions are clarified. We also confirm the existence of period-doubling cascades and chaotic attractors in experimental laboratory

Neuromodulation of Neuromorphic Circuits

We present a novel methodology to enable control of a neuromorphic circuit in close analogy with the physiological neuromodulation of a single neuron. The methodology is general in that it only relies on a parallel interconnection of elementary voltage-controlled current sources. In contrast to controlling a nonlinear circuit through the parameter tuning of a state-space model, our approach is purely input-output. The circuit elements are controlled and interconnected to shape the current-voltage characteristics (I-V curves) of the circuit in prescribed timescales. In turn, shaping those I-V curves determines the excitability properties of the circuit. We show that this methodology enables both robust and accurate control of the circuit behavior and resembles the biophysical mechanisms of neuromodulation. As a proof of concept, we simulate a SPICE model composed of MOSFET transconductance amplifiers operating in the weak inversion regime.The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet n.67064

An analogue approach for the processing of biomedical signals

Constant device scaling has signifcantly boosted electronic systems design in the digital domain enabling incorporation of more functionality within small silicon area and at the same time allows high-speed computation. This trend has been exploited for developing high-performance miniaturised systems in a number of application areas like communication, sensor network, main frame computers, biomedical information processing etc. Although successful, the associated cost comes in the form of high leakage power dissipation and systems reliability. With the increase of customer demands for smarter and faster technologies and with the advent of pervasive information processing, these issues may prove to be limiting factors for application of traditional digital design techniques. Furthermore, as the limit of device scaling is nearing, performance enhancement for the conventional digital system design methodology cannot be achieved any further unless innovations in new materials and new transistor design are made. To this end, an alternative design methodology that may enable performance enhancement without depending on device scaling is much sought today.Analogue design technique is one of these alternative techniques that have recently gained considerable interests. Although it is well understood that there are several roadblocks still to be overcome for making analogue-based system design for information processing as the main-stream design technique (e.g., lack of automated design tool, noise performance, efficient passive components implementation on silicon etc.), it may offer a faster way of realising a system with very few components and therefore may have a positive implication on systems performance enhancement. The main aim of this thesis is to explore possible ways of information processing using analogue design techniques in particular in the field of biomedical systems

Asymptotic solvers for second-order differential equation systems with multiple frequencies

In this paper, an asymptotic expansion is constructed to solve second-order dierential equation systems with highly oscillatory forcing terms involving multiple frequencies. An asymptotic expansion is derived in inverse of powers of the oscillatory parameter and its truncation results in a very eective method of dicretizing the dierential equation system in question. Numerical experiments illustrate the eectiveness of the asymptotic method in contrast to the standard Runge-Kutta method