Modeling and Stability Analysis of Salmon Mortality due to Microalgae Bloom using Linear Parameter-Varying Structure

This paper investigates a non-autonomous system that describes a biomathematical model in a salmon farming context. More precisely, we consider two coupled nonlinear differential equations that model the dynamic behavior among aquatic pollution, salmon and microalgae populations. In this maritime habitat, we represent a harmful algal bloom (HAB) due to the climate event called El Niño. This phenomenon produces an ecological problem increasing the water temperature that starts a HAB, increasing the salmon mortality due to microalgae toxins and, consequently, incorporating additional aquatic pollution. In this work, we provide some stability and error analysis techniques based on a linear parameter-varying system modeling. Finally, we present numerical results and computational simulations in order to illustrate the applicability for our approach to model real ecological problems.