A discrete-time dynamical system and an evolution algebra of mosquito population

Recently, continuous-time dynamical systems of mosquito populations have been studied. We discuss a discrete-time dynamical system, generated by an evolution quadratic operator of a mosquito population. We construct an evolution algebra, taking its matrix of structural constants equal to the Jacobian of the quadratic operator at a fixed point. Idempotent and absolute nilpotent elements, simplicity properties, and some limit points of the evolution operator corresponding to the evolution algebra will be given.