Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model.
BACKGROUND
Development of effective and plausible numerical tools is an imperative task for thorough studies of nonlinear dynamics in life science applications.


RESULTS
We have developed a complementary suite of computational tools for two-parameter screening of dynamics in neuronal models. We test a 'brute-force' effectiveness of neuroscience plausible techniques specifically tailored for the examination of temporal characteristics, such duty cycle of bursting, interspike interval, spike number deviation in the phenomenological Hindmarsh-Rose model of a bursting neuron and compare the results obtained by calculus-based tools for evaluations of an entire spectrum of Lyapunov exponents broadly employed in studies of nonlinear systems.


CONCLUSIONS
We have found that the results obtained either way agree exceptionally well, and can identify and differentiate between various fine structures of complex dynamics and underlying global bifurcations in this exemplary model. Our future planes are to enhance the applicability of this computational suite for understanding of polyrhythmic bursting patterns and their functional transformations in small networks.
Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, 30303, USA. ashilnikov@gsu.edu.
Roberto
R
Barrio
Andrey
A
Shilnikov