Dynamics of a new stage-structured population model with transient and nontransient impulsive effects in a polluted environment

In this paper, we consider a new stage-structured population model with transient and nontransient impulsive effects in a polluted environment. By using the theories of impulsive differential equations, we obtain the globally asymptotically stable condition of a population-extinction solution; we also present the permanent condition for the investigated system. The results indicate that the nontransient and transient impulsive harvesting rate play important roles in system permanence. Finally, numerical analyses are carried out to illustrate the results. Our results provide effective methods for biological resource management in a polluted environment.

An analysis on the controllability and stability to some fractional delay dynamical systems on time scales with impulsive effects

In this article, we establish a new class of mixed integral fractional delay dynamic systems with impulsive effects on time scales. We investigate the qualitative properties of the considered systems. In fact, the article contains three segments, and the first segment is devoted to investigating the existence and uniqueness results. In the second segment, we study the stability analysis, while the third segment is devoted to investigating the controllability criterion. We use the Leray–Schauder and Banach fixed point theorems to prove our results. Moreover, the obtained results are examined with the help of an example.

Functional Coupled Systems with Generalized Impulsive Conditions and Application to a SIRS-Type Model

In this paper, we consider a first-order coupled impulsive system of equations with functional boundary conditions, subject to the generalized impulsive effects. It is pointed out that this problem generalizes the classical boundary assumptions, allowing two-point or multipoint conditions, nonlocal and integrodifferential ones, or global arguments, as maxima or minima, among others. Our method is based on lower and upper solution technique together with the fixed point theory. The main theorem is applied to a SIRS model where to the best of our knowledge, for the first time, it includes impulsive effects combined with global, local, and the asymptotic behavior of the unknown functions.