a. Obtained some sufficient criteria for dissipativity, persistence, permanence of ecological models.
b. Generalize the predator–prey models with Beddington–DeAngelis functional response and proved existence their periodic solution.
c. Showed that some sufficient criteria for globally asymptotically stable of ecological models.
d. Presented the conditions ensuring existence and uniqueness of positive bounded solution, positive periodic and almost periodic solution of population described by linear and non-linear differential equations.
e. Showed a stability radii formula of age–structured population described by homogeneous Lotka–Von Foerster system and the classical model of linear age-dependent population dynamics of Sharpe-Lotka-Mc Kendrick.
Furthermore, we illustrated the results by some numerical solutions for our systems.
