Weakly reversible single linkage class realizations of polynomial dynamical systems: an algorithmic perspective. (English) Zbl 07796566
Summary: Systems of differential equations with polynomial right-hand sides are very common in applications. In particular, when restricted to the positive orthant, they appear naturally (according to the law of mass-action kinetics) in ecology, population dynamics, as models of biochemical interaction networks, and models of the spread of infectious diseases. Their mathematical analysis is very challenging in general; in particular, it is very difficult to answer questions about the long-term dynamics of the variables (species) in the model, such as questions about persistence and extinction. Even if we restrict our attention to mass-action systems, these questions still remain challenging. On the other hand, if a polynomial dynamical system has a weakly reversible single linkage class \((WR^1)\) realization, then its long-term dynamics is known to be remarkably robust: all the variables are persistent (i.e., no species goes extinct), irrespective of the values of the parameters in the model. Here we describe an algorithm for finding \(WR^1\) realizations of polynomial dynamical systems, whenever such realizations exist.
MSC:
| 37N25 | Dynamical systems in biology |
| 34C07 | Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations |
| 92E20 | Classical flows, reactions, etc. in chemistry |
| 92D25 | Population dynamics (general) |
| 92D40 | Ecology |
| 92D30 | Epidemiology |
| 80A32 | Chemically reacting flows |
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