PMC:1570349 / 10675-11304 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/1570349","sourcedb":"PMC","sourceid":"1570349","source_url":"https://www.ncbi.nlm.nih.gov/pmc/1570349","text":"Consider the splitting of m-dimensional parameter space P ⊂ ℝm into input and system parameters, p = (pi, ps) ∈ Pi × ps . For an ODE system, let Σ denote a bifurcation manifold of interest, consisting of sets in parameter space P for which structural stability breaks down [1]. For a given system parameter ps, we further define Σ(ps) ≡ Σ ∩ {ps} as the intersection of Σ with the ps-plane. In Figure 2, the geometric relationship between Σ and Σ(ps) is illustrated. Let the forward operator F :P → P be a mapping in parameter space, taking a given point to its orthogonal projection on Σ(ps), assumed to be well-defined. That is,","tracks":[]}