Yes, there are mathematical models of oscillatory chemical reactions with three ordinary differential equations (ODEs) where two variables are fast and one is slow, exhibiting bursting behavior. A suitable example is a modified Brusselator model, adapted to include a slow inhibitor variable that modulates the fast oscillations. Below is a concrete formulation:

**Modified Brusselator Model wi...

Yes. There are several well‑studied chemical oscillator models with exactly three ODEs in a two‑fast/one‑slow (2F–1S) time‑scale structure that exhibit bursting or, in the chemical literature, mixed‑mode oscillations (MMOs: alternating epochs of small/fast oscillations and slow drifts or quiescence). Three prototypical examples are:

• Three‑variable Oregonator (Belousov–Zhabotinsky reaction)
  • ...

Yes – several well-studied chemical oscillators are described by exactly three ordinary differential equations in which two dynamical variables evolve on a fast time-scale and a third one changes much more slowly. When the parameters are chosen appropriately these systems show mixed–mode oscillations and true “bursting’’: episodes of rapid small-amplitude oscillations separated by long quiescent ...

Mathematical Models of Oscillatory Chemical Reactions with Two Fast Variables and One Slow Variable

For your specific need of a three-variable system with two fast variables, one slow variable, and bursting behavior, here are several promising chemical models:

1. Modified Glycolytic Oscillator Models

Glycolytic oscillations offer an excellent starting point. The standard two-variable model...

Yes – most of the small kinetic schemes that have been used for the Belousov-Zhabotinsky (BZ) reaction and for a number of related inorganic oscillators are of the form

dx/dt = F(x , y , z) dy/dt = G(x , y , z) dz/dt = ε H(x , y , z) 0 < ε ≪ 1 (1)

so that x and y vary on the fast time scale t and z varies on the slow time scale T = ε t.
When the fast 2-D subsystem (ε = 0)...

Bursting is a dynamical phenomenon often observed in systems with multiple time scales. In the context of chemical reactions, one classic example that fits this de...

Here is a brief catalogue of three‐variable chemical–kinetic models in which two species evolve on a “fast” time–scale and a third species (or an external parameter) evolves much more slowly, and which have in fact been shown to display “bursting’’ or mixed–mode oscillations. In almost all of them the slow variable modulates the excitability of an underlying two–dimensional oscillator, so that on...

You're looking for a specific type of chemical oscillator with particular dynamics - two fast variables and one slow variable that exhibits bursting behavior. While the classic Belousov-Zhabotinsky (BZ) reaction models don't fit your criteria, there are several chemical systems that do.

The Boissonade-De Kepper Model

One of the most relevant models for your needs is the **Boissonade-De Kepper...

Of course! This is an excellent question that sits at the intersection of chemical kinetics and dynamical systems theory. You are correct that many well-known chemical oscillators, when modeled, fall into the 1-fast/2-slow category. However, the 2-fast/1-slow structure you're looking for is a classic paradigm for generating bursting oscillations in many fields, including chemistry and neurobiology...