Paper Info
Title
A framework for modeling and analysis of dynamical properties of spiking neurons
Abstract
A hybrid systems framework for modeling and analysis of robust stability of spiking neurons is proposed. The framework is developed for a population of n interconnected neurons. Several well-known neuron models are studied within the framework, including both excitatory and inhibitory simplified Hodgkin-Huxley, Hopf, and SNIPER models. For each model, we characterize the sets that the solutions to each system converge to. Using Lyapunov stability tools for hybrid systems, the stability properties for each case are established. An external stimuli is introduced to the simplified Hodgkin-Huxley model to achieve a global asymptotic stability property. Due to the regularity properties of the data of the hybrid models considered, the asserted stability properties are robust to small perturbations. Simulations provide insight on the results and the capabilities of the proposed framework.
Year
DOI
Venue
2014
10.1109/ACC.2014.6859494
American Control Conference
Keywords
DocType
ISSN
Lyapunov methods,asymptotic stability,neural nets,Hopf models,Lyapunov stability tools,SNIPER models,dynamical properties,global asymptotic stability property,hybrid systems,hybrid systems framework,neuron models,robust stability,simplified Hodgkin-Huxley models,spiking neurons,Biological systems,Hybrid systems,Stability of hybrid systems
Conference
0743-1619
Citations 
PageRank 
References 
1
0.44
4
Authors
2
Name
Order
Citations
PageRank
Sean Phillips1154.66
Ricardo G. Sanfelice221627.88