Cusp Bifurcation in Metastatic Breast Cancer Cells

Brenda Delamonica, Gábor Balázsi, Michael Shub

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper and the model both define the cusp via the same 5×5 system [V=0, det(DxV)=0, ∇x det(DxV)·v=0 with v in ker DxV], locate essentially the same numerical solution near (R,L,B,ρ,k)≈(0.9321,2.2184,0.0435,1.0281,0.1343), verify nondegeneracy (invertible 5×5 Jacobian), and invoke standard cusp normal-form theory to conclude the local one-versus-three equilibria geometry and pitchfork along the cusp tangent. The approaches and conclusions agree in substance and detail.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

This manuscript applies standard cusp bifurcation theory to a biologically motivated ODE model of metastatic transitions, offering a coherent synthesis between numerical evidence (Newton/MATCONT) and qualitative bifurcation geometry. The central claim—existence of a cusp and its implications (one vs. three equilibria, pitchfork along tangent, hysteresis)—is supported by a consistent computational pipeline and standard theory. Revisions should clarify parameter scaling ("expected" vs. computed cusp) and provide a brief note on numerical conditioning and nondegeneracy checks to strengthen reproducibility and rigor.