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10 September 2007 Modeling the brain with laser diodes
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Abstract
The Wilson-Cowan mathematical model is popular for representing a neuron in the brain and may be viewed as two cross-coupled dynamical nonlinear neural networks, one excitatory and one inhibitory. This gives rise to two coupled first order equations. Varying an input parameter, the sum of input intensities from all other incoming neurons, causes the Wilson-Cowan neural oscillator to move through a supercritical Hopf bifurcation so as to switch its output from a stable-off when the input is below a firing threshold to a stable-oscillation (limit cycle) for signals above the threshold; the frequency of which depends on the level of input stimulation. The use of frequency to represent pulse rate makes the brain robust against electromagnetic interference and drift. We show that the laser diode rate equations for a single optically injected laser diode can also be modeled by two coupled first order equations that give rise to supercritical Hopf bifurcations. But the laser rate equations have a complex variable where that for the Wilson-Cowan model equations is real. By using the real part of the complex variable (a projection onto the real plane), the optically injected laser diode can exactly simulate the movement through supercritical Hopf bifurcation of the Wilson-Cowan equations by varying the amplitude and frequency of the optical injection.
© (2007) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Alastair D. McAulay "Modeling the brain with laser diodes", Proc. SPIE 6775, Active and Passive Optical Components for Communications VII, 67750B (10 September 2007); https://doi.org/10.1117/12.733183
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