  Spiking neural network models characterize the emergent collective dynamics
of circuits of biological neurons and help engineer neuro-inspired solutions
across fields. Most dynamical systems' models of spiking neural networks
typically exhibit one of two major types of interactions: First, the response
of a neuron's state variable to incoming pulse signals (spikes) may be additive
and independent of its current state. Second, the response may depend on the
current neuron's state and multiply a function of the state variable. Here we
reveal that spiking neural network models with additive coupling are equivalent
to models with multiplicative coupling for simultaneously modified intrinsic
neuron time evolution. As a consequence, the same collective dynamics can be
attained by state-dependent multiplicative and constant (state-independent)
additive coupling. Such a mapping enables the transfer of theoretical insights
between spiking neural network models with different types of interaction
mechanisms as well as simpler and more effective engineering applications.
