Phase plane (left) of an action potential generated by the FitzHugh–Nagumo model. Neural dynamics is largely concerned with understanding how such action potentials arise from the underlying biophysical and network dynamics. However, it also goes beyond and studies the dynamics of, e.g., neuronal populations, synaptic plasticity, and learning. In this post, we provide a definitional overview of the field of neural dynamics in order to situate it within the broader context of computational neuroscience and clarify some common misconceptions.

Spiking activity in a recurrent network of model neurons (Izhikevich model). Shown are the spike times of all neurons in a recurrent spiking neural network as a function of time. The network consists of 800 excitatory neurons with regular spiking (RS) dynamics and 200 inhibitory neurons with low-threshold spiking (LTS) dynamics, separated by the horizontal line. Each vertical mark corresponds to an action potential (spike) emitted by a single neuron. In the context of neural dynamics, this representation illustrates how single-neuron events, such as the action potentials described above, combine to form structured, time-dependent activity patterns at the network level. Such spiking rasters provide a direct link between microscopic neuronal dynamics and emerging population activity, which can later be analyzed in terms of collective states, low-dimensional structure, and neural manifolds.

Two complementary perspectives on population activity in neural dynamics. The figure contrasts a “circuit” perspective with a “neural manifold” perspective. In circuit models, neurons are organized in an abstract tuning space, where proximity reflects tuning similarity, and recurrent connectivity W i j together with external inputs generates time-dependent firing rates r i ( t ) (panels A–C). In the neural manifold view, the joint activity vector r ( t ) ∈ R N of a recorded population evolves along low-dimensional trajectories embedded in a high-dimensional space (panels D–F). This is illustrated by ring-like manifolds for head-direction representations and by rotational trajectories in motor cortex, both of which can often be captured by a small number of latent variables κ 1 ( t ) , … , κ D ( t ) with D ≪ N . In the context of our overview post here, I think, the figure highlights very well why neural dynamics naturally connects mechanistic network modeling with state-space descriptions of population activity. These are not competing accounts, but complementary levels of description that emphasize different aspects of the same underlying dynamical system. Source: Figure 1 from Pezon, Schmutz, Gerstner, Linking neural manifolds to circuit structure in recurrent networks, 2024, bioRxiv 2024.02.28.582565, DOI: 10.1101/2024.02.28.582565ꜛ (license: CC-BY-NC-ND 4.0)