Scenarios for the appearance of strange attractors in a model of three interacting microbubble contrast agents

The paper presents careful numerical evidence and proposes plausible mechanisms (successive flip or Neimark–Sacker bifurcations of embedded saddles for the +++ onset; partial synchrony inducing a quasi-periodic-like drive for the additional zero), but explicitly stops short of a proof and cannot continue the relevant periodic orbits. The model solution formalizes these scenarios with symmetry, NHIM, and skew-product arguments, and adds a decoupling-limit route to +++ hyperchaos, yet it relies on unproven persistence/continuity of Lyapunov exponents and makes at least one incorrect scaling/limit claim. Net: both accounts illuminate the phenomena but neither provides a complete, rigorous argument.