Dynamical Behavior of a Juvenile Predator, Adult Predator and Prey Model Through Uncertain and Parametric Technique

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In this study, an interaction model involving a juvenile predator, an adult predator, and the prey has been developed. It is considered that juvenile predators are unable to reproduce. The adult predator is considered to have an impact on the growth rate of the juvenile predators. It is also assumed that a portion of juvenile predators may become adults. Also, it is considered that adult predators consume prey for food. The logistic growth of prey has been taken into consideration in the absence of an adult predator. The intra-species competition among adult predators is discussed here. It is also assumed that adult predators could chase and eat juvenile predators. Then most of the parametric values are considered interval-valued uncertain numbers. Since it is very hard for us to solve the model when the parametric values are interval-valued. Thus, all of the interval-valued parameters have been simplified into linear parametric form. After that, the nonnegativity and boundedness of the model were discussed. Various possible equilibrium points in the model are analyzed. The model’s local stability and global stability are investigated near these points. It has been noted that the proposed model’s solution is significantly impacted by the uncertain values of the model parameters. Uncertain estimates of intra-species competition among adult predators have been found to have a considerable impact on the stability of the model. It is observed that the increased uncertainty of intra-species competition for prey may stabilize the system. It is reported that the increasing rate of conversion of prey into adult predators can destabilize the ecosystem. It is found that the increasing rate of predation on juvenile predators by adults reduces the number of juveniles that can mature into adults which may create instability in the system.