6 problems

Let the PAVD model be the preferential attachment model with vertex death from Definition. Suppose that the attachment and death-rate sequences $b$ and $d$ satisfy Assumptions and.…

Persistence Conjecture. Every weakly reversible mass action system is persistent.

A weakly reversible mass-action kinetics ODE system is a system whose reaction network is weakly reversible, with dynamics governed by mass-action kinetics. A system is persistent…

Let $N$ be a confined, weakly reversible mass-action ordinary differential equation system, and let $\mathfrak M^\ell(N)$ denote its associated differential inclusion. A differenti…

Consider the structured stochastic difference equation … is almost surely persistent and persistent in probability. A theorem establishes this conclusion under the stronger monoton…

Consider the two-species Markov chain … is almost surely persistent. Mutual invasibility is known to imply persistence in probability under the monotonicity assumptions; the conjec…