New topological classification of bursting in multi-time-scale Chay-Cook model

Various waveforms of bursting discharges in dynamical models with multiple time scales always imply complex dynamical behaviors, and so it is important but difficult to survey their topological types by multi-layered fast-slow analyses. In this work, we find out two parameters in the Chay-Cook model, which together enable to change timescale of a variable in the model from fast to medium-slow to slow to control directly and indirectly timescales of the system, respectively. At two moderate values of one parameter controlling directly timescales, a variety of complex bursting discharges are excavated by increasing another parameter controlling indirectly timescales to slow the variable down. Thus, two different fast-slow analyses are combined to define more accurately topological types of the bursting discharges. The new definition of the topological type of bursting proposed in the work is an extension and improvement of the existing classification, and provides a dynamic basis for further study of the complexity of information encoding in neuronal system.

Automated summary

This study investigates the topological types of bursting discharges in dynamical models with multiple time scales using multi-layered fast-slow analysis. Two parameters are identified in the Chay-Cook model that control the timescales of the system. By combining two different fast-slow analyses, the researchers define the topological types of bursting discharges more accurately. This new definition extends the existing classification and provides a dynamic basis for studying the complexity of information encoding in neuronal systems.