Proves parameter-space partitions into regions with unique stable equilibria in n-strain models via explicit Perron-Volterra Lyapunov functions for boundary and coexistence equilibria.
Global stability of first order endotactic reaction systems
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The work extends a strong threshold theorem for balanced bilinear models in mathematical epidemiology, showing equilibrium existence via a spectral radius condition on a state-dependent next-generation matrix and classifying eigenvector-based Lyapunov constructions.
A linear Lyapunov function provides a checkable condition for non-explosivity of CTMCs and global existence of ODEs in reaction systems, proving regularity for second-order endotactic and bimolecular weakly reversible mass-action systems.
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Perron-Volterra Lyapunov functions and competitive exclusion partitions in n-strain models with diagonal Metzler transversal Jacobian and rank-one blocks
Proves parameter-space partitions into regions with unique stable equilibria in n-strain models via explicit Perron-Volterra Lyapunov functions for boundary and coexistence equilibria.
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A Perron-Frobenius strong threshold theorem for (A, B, P, {\phi}) balanced bilinear models, and the role of left and right Perron eigenvectors in mathematical epidemiology
The work extends a strong threshold theorem for balanced bilinear models in mathematical epidemiology, showing equilibrium existence via a spectral radius condition on a state-dependent next-generation matrix and classifying eigenvector-based Lyapunov constructions.
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On the Regulary of Reaction Systems
A linear Lyapunov function provides a checkable condition for non-explosivity of CTMCs and global existence of ODEs in reaction systems, proving regularity for second-order endotactic and bimolecular weakly reversible mass-action systems.