Topic: multistability

The nervous system is fundamentally a closed loop control device: the output of actions continually influences the internal state and subsequent actions. This is true at the single cell and even the molecular level, where “actions” take the form of signals that are fed back to achieve a variety of functions, including homeostasis, excitability and various kinds of multistability that allow switching and storage of memory. It is also true at the behavioural level, where an animal’s motor actions directly influence sensory input on short timescales, and higher level information about goals and i

Threshold-linear networks (TLNs) display a wide variety of nonlinear dynamics including multistability, limit cycles, quasiperiodic attractors, and chaos. Over the past few years, we have developed a detailed mathematical theory relating stable and unstable fixed points of TLNs to graph-theoretic properties of the underlying network. In particular, we have discovered that a special type of unstable fixed points, corresponding to "core motifs," are predictive of dynamic attractors. Recently, we have used these ideas to classify dynamic attractors in a two-parameter family of inhibition-dominate

Interactions between spiking units grouped in distinct excitatory (E) and inhibitory (I) populations can result in a complex dynamical landscape. Part of this complexity, namely dynamics that depend on undelayed connectivities and external inputs, is retained by a simplified model, the threshold-linear network (TLN), which allows to derive fully analytical conditions for the emergence of multistability [1], paradoxical perturbation effects [2,3], and some oscillations [4,5]. These results, however, have only been applied to specific architectures, such as canonical circuits or all-inhibitory n