In collaboration with Dr. Nikolai Rulkov we develop a new computationally efficient approach to analyze large-scale networks of biological neurons. This approach is based on using difference equations (map) for simulation of neuron dynamics. The nonlinear maps produce very rich spectrum of dynamical behaviors while remaining simple and low-dimensional systems and, therefore, can be very computationally efficient. Conventional approach based on simulating ordinary differential equations (such as Hodgkin-Huxley type models) quickly reaches its limit when the number of elements in the network increases. It makes this approach impractical for studying those problems when the analyzed phenomena originates from a collective behavior of large neural ensembles. A map-based model of a neuron that realistically replicates the dynamical mechanisms underlying both its spiking and bursting activity and correctly captures the input-output processes opens new opportunities in the studies of large-scale network functionality. This approach will provide the basis for network simulations of different brain systems, including hundreds of thousands neurons, at the realistic time scales using conventional workstations.
Example of C++ code to simulate spiral wave dynamics in 2D network of regular spiking neurons and fast spiking interneurons:
C++ code to simulate 2D network - network2D.cpp.txt
Input file for network simulations - input2D.txt
To compile the code using GCC compiler: gcc network2D.cpp -lm -O2 -o network2D
To run simulations: network2D input2D.txt > tmp
Click here to see movie of spiral wave dynamics. These neuron and network models are discussed in N.Rulkov, I.Timofeev and M.Bazhenov. Oscillations in large-scale cortical networks: map-based model. Journal of Computational Neuroscience 17, 203–223, 2004