Bifurcations Dynamics of Single Neurons and Small Networks
A bifurcation occurs when a system undergoes a qualitative change in its output as a result of a change in parameter. Under certain conditions, the voltage of a cell membrane can change from being at rest to becoming oscillatory as a result of a bifurcation. Oscillatory properties of small networks are often understood using bifurcation analysis.
What Is a Bifurcation?
The word bifurcate is commonly used to denote a split, as in “up ahead, the road bifurcates into two parts.” The use of the term in this context implies that a driver traveling on this road can make a real-time choice of being able to take one or the other branch of the road when the bifurcation point is reached. In mathematics, and in its application to neuroscience, the term bifurcation has an entirely different contextual meaning. While a mathematical bifurcation is similar in that it involves different branches, the decision on which branch is chosen is largely made a priori and depends on the...
KeywordsPeriodic Orbit Hopf Bifurcation Bifurcation Diagram Bifurcation Analysis Pitchfork Bifurcation
This work was supported in part by NSF DMS 1122291.
- Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. In: Teramoto E, Yamaguti M (eds) Mathematical topics in population biology, morphogenesis and neurosciences, vol 71, Lecture notes in biomathematics. Springer, New YorkGoogle Scholar