Neurons, Models, and Invariants

  • Mario NegrelloEmail author
Part of the Springer Series in Cognitive and Neural Systems book series (SSCNS, volume 1)


The theory of dynamical systems is presented as an integrative theory, as it offers a consistent method to cross levels and scales. Behavior happens in recurrent loops where what happens next is what happened before plus how things work. Dynamical systems abstracts organisms into state variables, rules, and parameters. Analysis of structure and parameters can be done both analytically and computationally to address the invariances of a modeled system. Dynamical systems analysis reveals new facets of the phenomena modeled, and may effectively lead to powerful reductions. The Hodgkin–Huxley model of the action potential is presented as a prototypical example of dynamical systems analysis applied to neurons. The Hodgkin–Huxley model illustrates several interesting aspects of action potential generation, for example, how constancy in the action potentials appears despite variability in ion channel distribution. Effectively, dynamical systems modeling demonstrates how a phenomenon can be analyzed with respect to its parameters and structure, and helps solve the dichotomy between constancy and variability through mappings between parameter domains and dynamical varieties.


Logical Operation Patch Clamp Recurrent Neural Network Neural Model Parameter Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Okinawa Institute of Science and TechnologyOkinawaJapan

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