Threshold-linear networks (TLNs) are common models in theoretical neuroscience that are useful for modeling neural activity and computation in the brain. They are simple, recurrently-connected networks with a rich repertoire of nonlinear dynamics including multistability, limit cycles, quasiperiodic attractors, and chaos. Surprisingly, the same dynamic attractor can arise in multiple TLNs with distinct architectures and dynamics, and is preserved across large swaths of the TLN parameter space. We will also see how ideas from oriented matroids allow us to study the bifurcation theory of TLNs, providing valuable insights into the connection between network architecture and dynamics.

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