Local stability analysis of two density-dependent semelparous species in two age classes - Hasibuan, Arjun; Supriatna, Asep K.; Carnia, Ema (Frontiers in Applied Mathematics and Statistics, 2022)
It is crucial to take the dynamics of the species into account while investigating how a species may survive in an environment. A species can be classified as either semelparous or iteroparous depending on how it reproduces. In this paper we present a model of system consists of two semelparous species considering two classes of age. We specifically discuss the effects of density-dependent in the interaction between the two semelparaous species and look for the equilibria of the system in the absence and presence of harvesting to the system. Local stability of the equilibria is investigated. A modified Leslie matrix population model with the addition of density-dependent in the equation is used. The model is analysed in the presence and absence of competition between the species. We assume that density-dependent only occurred in the first age class of both species and that harvesting only occurred in the second age class for both species. Then, we assume that competition only occurs in the first age class in both species in the form of interspecific and intraspecific competition. This assumption is intended to simplify the complexity of the problem in the model. Our results show that there are three equilibria in the model without competition and four equilibria in the model with competition. Hence, the presence of competition has influenced the number of equilibria. We also investigate the relation between the stability of the equilibria with the net reproduction rate of the system. Furthermore, we found the condition for local stability of the co-exist equilibrium point related to the degree of interspecific competition and intraspecific competition intensities. The dynamics of natural resource models, including the impacts of various management on resource growth, such as in fisheries, may be studied using this theory.