EXPLORING THE EFFECT OF CLIMATE CHANGE VIA PARITY-BASED PULSED TIMES OF COSINUSOIDAL WAVES IN SUSTAINABLY CONTROLLED MARINE BIOSYSTEMS

In this paper, we consider trophic-halieutic systems which describe interactions between communities of grazers and predators in the presence of a compartment dedicated to the evolution of marine vegetation. The first system version is in the form of control differential equations. As we could not deny that most observations in this context may be collected at discrete times, we also explore those dynamics using the second system version and which takes the form of control difference equations despite the difficulty often met in their analysis, letting the literature focus on the continuous-time framework. Since it does not also seem that obvious to introduce the disruptions that may be caused by the climate change in such well-known and practical types of models, this work introduces the effect of such phenomena through bang-bang climate waves that we believe could be described using a periodic function like the cosine of πt with t the time variable and that takes the values of either 1 when the pulsed t of climate induced stability is an even number promoting the increase of the vegetation or -1 when the pulsed t of climate change is an odd number leading to the extinction of that biomass. In addition, as overfishing could also represent a direct cause to the disappearance of some fishes, our study investigates the behaviors of the marine species densities under harvesting efforts whose best values are sought through optimal control policies designed to conserve the populations of both forage and big fishes for the benefit of a sustainable environment.