2016/05/30 by Maria Luisa Saggio, Saggio, Maria Luisa, Andreas Spiegler +5 · 1 citation
Physics and Astronomy · Computer Science · #stochastic dynamics and bifurcation #Advanced Thermodynamics and Statistical Mechanics #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1605.09353
Bursting is a phenomenon found in a variety of physical and biological\nsystems. For example, in neuroscience, bursting is believed to play a key role\nin the way information is transferred in the nervous system. In this work, we\npropose a model that, appropriately tuned, can display several types of\nbursting behaviors. The model contains two subsystems acting at different\ntimescales. For the fast subsystem we use the planar unfolding of a high\ncodimension singularity. In its bifurcation diagram, we locate paths that\nunderly the right sequence of bifurcations necessary for bursting. The slow\nsubsystem steers the fast one back and forth along these paths leading to\nbursting behavior. The model is able to produce almost all the classes of\nbursting predicted for systems with a planar fast subsystems. Transitions\nbetween classes can be obtained through an ultra-slow modulation of the model's\nparameters. A detailed exploration of the parameter space allows predicting\npossible transitions. This provides a single framework to understand the\ncoexistence of diverse bursting patterns in physical and biological systems or\nin models.\n