Modeling the chaos in a neuron

When neurons transmit messages throughout the body through electrical currents, the currents can be regular and rhythmic, or irregular, chaotic bursts.

Using a model inspired by the Hodgkin-Huxley framework, which treats pieces of a neuron like electrical components, Scully et al. investigated how chaos arises within a biologically realistic neuron model.

While using this model to study swimming rhythms in sea slugs, the researchers discovered an unusually large region of chaotic activity. Like a kaleidoscope, chaos in neurons can be described as a small seed that fragments and replicates into widespread complexity.

This discovery was interesting, since chaotic dynamics are typically confined to narrow regions near transitions between different neuronal behaviors.

“We began studying the chaotic behavior patterns out of curiosity and quickly recognized that they did not match our previous knowledge of neuronal chaos,” said author Jack Scully.

Using advanced computational tools, they reduced the complexity of the model into an intuitive, one-dimensional map.

They explained that the chaos was prevalent near Shilnikov-Hopf points. These points occur where the saddle focus equilibrium point undergoes a Hopf bifurcation, in which the system’s stability changes, and has a homoclinic orbit, a trajectory that begins and ends at the saddle focus over time.

Their findings offer fresh perspectives on how neurons can naturally generate broad and resilient chaotic dynamics, challenging traditional ideas about neuronal stability and adaptability. The researchers plan to extend this modeling to other neuronal models, but the tools presented in the paper have other uses; for instance, the techniques can be used to model various types of complex dynamical systems.

“Studying rich classes of global bifurcations is very achievable with the right tools,” Scully said.

Source: “Widespread neuronal chaos induced by slow oscillating currents,” by James Scully, Carter Hinsley, David Bloom, Hil G.E. Meijer, and Andrey L. Shilnikov, Choas (2025). The article can be accessed at https://doi.org/10.1063/5.0248001 .