  We study the dynamics of two symmetrically coupled populations of identical
leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon
varying the coupling strength, we find symmetry-breaking transitions that lead
to the onset of various chimera states as well as to a new regime, where the
two populations are characterized by a different degree of synchronization.
Symmetric collective states of increasing dynamical complexity are also
observed. The computation of the the finite-amplitude Lyapunov exponent allows
us to establish the chaoticity of the (collective) dynamics in a finite region
of the phase plane. The further numerical study of the standard Lyapunov
spectrum reveals the presence of several positive exponents, indicating that
the microscopic dynamics is high-dimensional.
