Complex-valued computational model of hippocampal CA3 recurrent collaterals

Complex planes are known to simplify the complexity of real world problems, providing a better comprehension of their functionality and design. The need for complex numbers in both artificial and biological neural networks is equally well established. In the latter, complex numbers allows neuroscientists to consider and analyze the phase component of brain oscillations occurring during chains of action potentials. This paper implements complex-valued weights and inputs in the real valued recurrent collaterals model introduced by Káli & Dayan for the CA3 region of the hippocampus, with equations appropriately modified to include the phase component. Complex models can generally be implemented by solving the real and complex parts separately resulting from solving the model equations twice. This implementation is simulated here and the results demonstrate the model's potential utility for further mathematical and neurobiological analysis to define a proper phase function which oscillates in the theta frequency range.