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Izhikevich Neuron Model equations implemented in 22-Bit on Verilog

The project implements neuron behaviors based on the Izhikevich equation. The internal operations work on a 22-bit Q3.18 fixed format. To achieve accurate neuron behavior, the original equations have been modified as shown below.

How it works

The model combines the biological realism of Hodgkin-Huxley-type dynamics with the computational efficiency of integrate-and-fire neurons, enabling the simulation of spiking cortical neurons. However, working with digital circuits presents challenges in executing the necessary operations for Euler integration methods, as noted by Nadiri Andabili, Nazari, and Moosazadeh (2025). To address these issues, the following Izhikevich Neuron Model equations were proposed based on the findings of Nadiri Andabili, Nazari, and Moosazadeh (2025)

V_m' = 4V_m^2 + 5V_m + 1.3947 - 0.3157U_m + I

U_m' = a(3.1666bV - (U_m+0.0166))

As a consequence, the operational range was changed from [-65, 30] to [-0.65, 0.30], also changing its reset to:

\text{if } V \geq V_{TH} \text{ then }
\begin{cases}
V_{old} \leftarrow c \\
V \leftarrow c \\
U_{old} \leftarrow U + d \\
U \leftarrow U + d
\end{cases}\\
\text{else}
\begin{cases}
V \leftarrow V_{old} \\
U \leftarrow U_{old}
\end{cases}

As a result, the following schematic was implemented. The SELECT pins function as a multiplexer, allowing the neuron behavior to be set to one of the options described in the 'Parameter Selection' section. The other five input pins represent a current, I, which is mapped from 0.0066 to 0.994. The sixteen output pins include eight that represent the membrane potential, V_out, in a fixed Q0.7 format, as well as another eight output bits for the membrane recovery variable. schematic

Parameter selection

Select	a	b	c	d	U	V
3'b000	0.02	0.20	0.65	8	0.20	0.65
3'b001	0.02	0.20	0.55	4	0.20	0.65
3'b010	0.02	0.20	0.50	2	0.20	0.65
3'b011	0.10	0.20	0.65	2	0.20	0.65
3'b100	0.02	0.25	0.65	0.05	0.25	0.65
3'b101	0.02	0.25	0.87	0.05	0.25	0.65
3'b110	0.10	0.25	0.65	2	0.25	0.65
3'b111	0.02	0.25	0.65	2	0.25	0.65

How to test

In the testbench, it is only necessary to set the operating frequency (10 MHz) and the input current I. In the end, results like the following should be obtained:

Salida del spike

External hardware

To externally observe the signals, it is necessary to invert the outputs V_out and U_out using NOT gates and connect them to an oscilloscope capable of performing bit-level measurements.

📑 "References (cited in the text)"

This model was proposed by Izhikevich (2003), and allows simulating various types of neurons by changing only the parameters a, b, c, and d.

📚 Referencias

Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14(6), 1569–1572. PDF
Izhikevich, E. M. (2004). Which model to use for cortical spiking neurons? IEEE Transactions on Neural Networks, 15(5), 1063–1070. PDF
M. Nadiri Andabili, S. Nazari, y T. Moosazadeh, “Chaotic dynamics analysis and digital hardware design of the Izhikevich neuron model,” Scientific Reports, vol. 15, art. 16766, 2025.

#	Input	Output	Bidirectional
0	select0	V_out0	U_out0
1	select1	V_out1	U_out1
2	select2	V_out2	U_out2
3	I0	V_out3	U_out3
4	I1	V_out4	U_out4
5	I2	V_out5	U_out5
6	I3	V_out6	U_out6
7	I4	V_out7	U_out7

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