Dynamics of non-Volterra quadratic operators: permuted and epidemic models

In this dissertation, we investigate discrete-time dynamical systems generated by non-Volterra quadratic operators from two distinct classes. The first class includes quadratic operators associated with permutations, while the second class consists of quadratic operators that represent a discrete version of the SIRD (Susceptible-Infected-Recovered-Deceased) epidemiological model. For each of these operators, we describe the set of periodic points and show that any orbit under these operators converges to either a fixed point or a periodic orbit.