A Low Dimensional Description of Globally Coupled Heterogeneous Neural Networks of Excitatory and Inhibitory Neurons

Neural networks consisting of globally coupled excitatory and inhibitory nonidentical neurons may exhibit a complex dynamic behavior including synchronization, multiclustered solutions in phase space, and oscillator death. We investigate the conditions under which these behaviors occur in a multidimensional parametric space defined by the connectivity strengths and dispersion of the neuronal membrane excitability. Using mode decomposition techniques, we further derive analytically a low dimensional description of the neural population dynamics and show that the various dynamic behaviors of the entire network can be well reproduced by this reduced system. Examples of networks of FitzHugh-Nagumo and Hindmarsh-Rose neurons are discussed in detail.Author Summary: Nowadays we know that most cognitive functions are not represented in the brain by the activation of a single area but rather by a complex and rich behavior of brain networks distributed over various cortical and subcortical areas. The communication between brain areas is not instantaneous but also undergoes significant signal transmission delays of up to 100 ms, which increase the computation time for brain network models enormously. In order to allow the efficient investigation of brain network models and their associated cognitive capabilities, we report here a novel, computationally parsimonious, mathematical representation of clusters of neurons. Such reduced clusters are called “neural masses” and serve as nodes in the brain networks. Traditional neural mass descriptions so far allowed only for a very limited repertoire of behaviors, which ultimately rendered their description biologically unrealistic. The neural mass model presented here overcomes this limitation and captures a wide range of dynamic behaviors, but in a computationally efficient reduced form. The integration of novel neural mass models into brain networks represents a step closer toward a computational and biologically realistic realization of brain function.