# Analog circuitry for the van der Pol and FitzHugh-Nagumo equations

@article{Keener1983AnalogCF, title={Analog circuitry for the van der Pol and FitzHugh-Nagumo equations}, author={James P. Keener}, journal={IEEE Transactions on Systems, Man, and Cybernetics}, year={1983}, volume={SMC-13}, pages={1010-1014} }

An analog circuit for the FitzHugh-Nagumo equations is given that uses readily available integrated circuitry. The mathematical model for this circuit is derived, and simple analysis is given, to show how the circuit works. Specifications for a reliable and easily built analog neuron are given with components that cost only a few dollars. The circuit is useful as a research and educational device.

#### Figures and Topics from this paper

#### 55 Citations

CIRCUIT IMPLEMENTATION OF NEURAL FITZHUGH-NAGUMO EQUATIONS

- Physics
- 1990

A circuit is proposed that emulates FitzHugh- Nagumo's differential equations using OTAs, diodes and ca- pacitors. These equations model the fundamental behavior of an organic neuron cell, i.e., if… Expand

Circuit implementation of neural FitzHugh-Nagumo equations

- Mathematics
- Proceedings of the 32nd Midwest Symposium on Circuits and Systems,
- 1989

A circuit that emulates FitzHugh-Nagumo's differential equations using OTAs, diodes, and capacitors is proposed. These equations model the fundamental behavior of an organic neuron cell, i.e. if the… Expand

A CMOS Implementation of Fitzhugh-Nagumo Neuron Model

- Engineering, Computer Science
- ESSCIRC '90: Sixteenth European Solid-State Circuits Conference
- 1990

Experimental results from a CMOS prototype are given that show the suitability of the technique used, and their potential for biological CMOS system emulation. Expand

A CMOS Implementation of FitzHugh-Nagumo

- Computer Science
- 1991

A complete derivation of neuron model is pre- sented, starting with the description of the fundamental biologi- cal mechanisms involved in the living neural cell, followed by the mathematical model… Expand

CMOS CIRCUIT IMPLEMENTATIONS FOR NEURON MODELS

- 2004

Discussion of the mathematical neuron basic cells employed in popular neural network architectures and algorithms are presented. From the fundamental Mc Culloch-Pitts model up to the resultant model… Expand

Non-monotonic firing rate of a coupled FitzHugh-Nagumo model

- Computer Science
- IEEE International Conference on Neural Networks
- 1993

An input-output relation of a neuron model consisting of two FitzHugh-Nagumo elements coupled through resistance is studied and it is shown that the firing rate of the neuron is a nonmonotonic function of the period of stimulus pulses when the coupling is weak. Expand

CMOS analog neural network systems based on oscillatory neurons

- Engineering
- [Proceedings] 1992 IEEE International Symposium on Circuits and Systems
- 1992

The authors discuss the design of two neural network systems based on the use of pulsing neurons. Each neuron was built as a simple voltage controlled oscillator (VCO) whose control voltage made the… Expand

CMOS circuit implementations for neuron models

- Computer Science
- IEEE International Symposium on Circuits and Systems
- 1990

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. Expand

Neuromorphic Design of a Bursting Circuit

- Computer Science
- 2018

As an input-output approach, I-V curve shaping proves effective in enabling robust and accurate control of the circuit behavior, suggesting a close analogy to the biophysical mechanisms of neuromodulation. Expand

Conceptual circuit models of neurons.

- Physics, Medicine
- Journal of integrative neuroscience
- 2009

It is shown that the simple analog models presented can reproduce known phenomena of membrane excitability such as the generation of action potentials and spike bursts. Expand

#### References

SHOWING 1-10 OF 21 REFERENCES

An Active Pulse Transmission Line Simulating Nerve Axon

- Physics
- Proceedings of the IRE
- 1962

To electronically simulate an animal nerve axon, the authors made an active pulse transmission line using tunnel diodes. The equation of propagation for this line is the same as that for a simplified… Expand

The Art of Electronics

- Engineering, Physics
- 1980

The new Art of Electronics retains the feeling of informality and easy access that helped make the earlier editions so successful and popular, and is an indispensable reference and the gold standard for anyone, student or researcher, professional or amateur, who works with electronic circuits. Expand

A mathematic model of automaticity in the sinus node and AV junction based on weakly coupled relaxation oscillators.

- Mathematics, Medicine
- Computers and biomedical research, an international journal
- 1977

The mathematical model reproduces satisfactorily the physiological results of experiments previously performed on dogs in this laboratory and is useful in both the design and analysis of biologic experiments to define most known determinants of either normal or abnormal cardiac rhythm. Expand

Traveling wave solutions of a nerve conduction equation.

- Physics, Medicine
- Biophysical journal
- 1973

The slower pulse is shown to be unstable and the faster one to be stable, confirming conjectures which have been made before for other nerve conduction equations, and the stability of the solutions is analyzed. Expand

Bifurcation of periodic motions in two weakly coupled van der Pol oscillators

- Physics
- 1980

Abstract We study a pair of weakly coupled van der Pol oscillators and investigate the bifurcations of phase-locked periodic motions which occur as the coupling coefficients are varied. Perturbation… Expand

Existence and Stability of Multiple Impulse Solutions of a Nerve Equation

- Mathematics
- 1982

A piecewise linear partial differential equation which models the propagation of a nerve impulse along an axon is studied. For the equation parameters used there are two solutions which represent… Expand

LXXII. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart

- Physics
- 1928

The mechanism of A-V arrhythmias; with an electronic analogue of the human A-V node.

- Medicine
- The American journal of medicine
- 1956

An hypothesis for the mechanisms of the A-V arrh rhythmias is advanced which explains many clinical aspects of these arrhythmias that have been perplexing in the past and is more consistent with modern excitation theory than are previous explanations. Expand

Mutually synchronized relaxation oscillators as prototypes of oscillating systems in biology

- Mathematics
- 1979

SummaryThis paper discusses the analogy between phenomena in populations of coupled biological oscillators and the behaviour of systems of synchronized mathematical oscillators. Frequency entrainment… Expand

Perturbation Methods in Applied Mathematics

- Mathematics
- 1969

1 Introduction.- 2 Limit Process Expansions Applied to Ordinary Differential Equations.- 3 Multiple-Variable Expansion Procedures.- 4 Applications to Partial Differential Equations.- 5 Examples from… Expand