  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.
