Dynamics and computation in mixed networks containing neurons that accelerate towards spiking
Networks in the brain consist of different types of neurons. Here we investigate the influence of neuron diversity on the dynamics, phase space structure and computational capabilities of spiking neural networks. We find that already a single neuron of a different type can qualitatively change the network dynamics and that mixed networks may combine the computational capabilities of ones with a single neuron type. We study inhibitory networks of concave leaky (LIF) and convex "anti-leaky" (XIF) integrate-and-fire neurons that generalize irregularly spiking non-chaotic LIF neuron networks. Endowed with simple conductance-based synapses for XIF neurons, our networks can generate a balanced state of irregular asynchronous spiking as well. We determine the voltage probability distributions and self-consistent firing rates assuming Poisson input with finite size spike impacts. Further, we compute the full spectrum of Lyapunov exponents (LEs) and the covariant Lyapunov vectors (CLVs) specifying the corresponding perturbation directions. We find that there is approximately one positive LE for each XIF neuron. This indicates in particular that a single XIF neuron renders the network dynamics chaotic. A simple mean-field approach, which can be justified by properties of the CLVs, explains the finding. As an application, we propose a spike-based computing scheme where our networks serve as computational reservoirs and their different stability properties yield different computational capabilities.
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