Abstract
We study the convex hulls of trajectories of polynomial dynamical systems. Such trajectories include real algebraic curves. The boundaries of the resulting convex bodies are stratified into families of faces. We present numerical algorithms for identifying these patches. An implementation based on the software Bensolve Tools is given. This furnishes a key step in computing attainable regions of chemical reaction networks.
Highlights
Dynamics and convexity are ubiquitous in the mathematical sciences, and they come together in applied questions in numerous ways
We explore an interaction of dynamics and convexity that is motivated by reaction systems in chemical engineering [9, 18]
We characterize planar algebraic curves that are trajectories of chemical reaction networks, we study the van de Vusse system [9, 18], and we exhibit a toric dynamical system [6] with convtraj(y) not forward closed
Summary
Dynamics and convexity are ubiquitous in the mathematical sciences, and they come together in applied questions in numerous ways. (ii) Decide whether the convex trajectory convtraj(y) is forward closed This happens if and only if the vector field φ(z) at every boundary point z points inwards, for every supporting hyperplane. We characterize planar algebraic curves that are trajectories of chemical reaction networks, we study the van de Vusse system [9, 18], and we exhibit a toric dynamical system [6] with convtraj(y) not forward closed.
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