Analysis of advection-diffusion-reaction model for fish population movement with impulsive tagging: stability and traveling wave solution

Abstract

So far, mobility in fish population has not been given sufficient attention, although movement and spatial heterogeneity can be an important dynamic feature that plays a critical role in their exploitation. Having a qualitative framework to describe and estimate movement and growth based on tagging data is necessary for efficient control and management of the fishing industry. Here, we construct an advection-diffusion-reaction model for the fish population structured to track the population densities of both the tagged fish and the tag-free fish, in which the impulsive tagging practice is incorporated, while continuous tagging is assumed to be done on off springs of trackable tagged fish, or on those in the same swarm as the trackable tagged fish. Using the traveling wave coordinate, we derive analytical expression for the solutions to the model system. We derive the explicit expression for the level of tagged fish which increases in a periodic impulsive fashion. Stability and phase plane analyses are also carried out to determine different behavior permitted by the model system.

A stage-structured delayed advection reaction-diffusion model for single species

“…Rattanakul [16] built an advection diffusion-reaction model demonstrate for the angle populace structured to track the populace densities of both the labeled angle and the tag-free angle, in which the rash labeling hone is joined, whereas nonstop labeling is accepted to be done on off springs of tractable labeled angle, or on those within the same swarm as the tractable labeled angle. Utilizing the traveling wave facilitate, they infer explanatory expression for the arrangements to the show framework.…”