Dale's law, stability and nonlinearity are sufficient constraints to ignite transient and self-sustained neural dynamics
The motor cortex orchestrates a rich and flexible repertoire of network dynamics for rhythmic and goal-directed movements. Computational studies have begun to illuminate the mechanistic origins of this repertoire, but a comprehensive model that can explain the emergence of both transient and self-sustained dynamics is still missing. Here, we show that three simple ingredients: Dalean connectivity, stability, and nonlinear neural responses, suffice to reverse-engineer networks that produce transient, steady-state, and self-sustained periodic activity. A single dynamical principle underlies this repertoire: the interaction of non-normal amplification, inherent to Dalean networks, with neuronal nonlinearity, so to ignite and sustain multi-stable, controllable dynamics. Our approach yields entire families of connectivity matrices that require no hand-tuning or learning of weights. Without fitting them to data, these networks reproduce the population-level signatures of motor cortex, implying that the richness of cortical dynamics need not be sculpted by learning, but may emerge from simple biological ingredients.