Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays

A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis.

• Publication year

  2012

• Venue

  Journal of Mathematical Neuroscience

• Publication date

  2012-04-25

• Fields of study

  Mathematics, Medicine

• Identifiers
  DOI 10.1186/2190-8567-2-8PMID 22655859PMCID 3478171
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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