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The primary aim of this research is to investigate how the presence of toxicity, stemming from phytoplankton, impacts fishing activities, catch levels, and financial returns. It is hypothesized that this toxicity arises when zooplankton accumulates harmful substances while consuming phytoplankton. To achieve this objective, we analyze a model resembling a prey-predator relationship involving phytoplankton. We examine the stable conditions in our model by utilizing eigenvalue analysis and calculate the optimal fishing effort that maximizes profitability for fishermen, employing the concept of generalized Nash equilibrium. Additionally, we explore the most effective harvesting strategy by applying Pontryagin's maximum principle. In our numerical simulations, we identify the key variables that influence all economic aspects of the model, including fishing effort, catch levels, and benefits. Furthermore, we compare our results with findings from previous research. [ABSTRACT FROM AUTHOR]

In this study, we delve into the complex interplay between the Allee effect and a tri-trophic marine ecosystem of zooplankton, sardines, and sharks in Moroccan waters, aiming to contribute to the field of coastal conservation, planning, and management. Our investigation focuses on understanding the impact of the Allee effect on catches, profits, and fishing efforts within the context of bioeconomic models. By analyzing the positive aspects, boundaries, and equilibrium points, we examine how the Allee effect influences the fishing efforts and overall performance of fishermen, providing valuable insights for sustainable fishing practices. The research outcomes shed light on the intricate interplay among the Allee effect, economic variables, and the abundance of diverse species, thereby offering crucial guidance for effective coastal conservation, planning, and management strategies. [ABSTRACT FROM AUTHOR]

The presence of populations potentially harmful dinoflagellate phytoplankton like Oxyrrhis marina requires vigilance and control, because these species, in high density or under certain conditions, can have serious economic consequences and a negative impact on public health. In this investigation, we formulate bioeconomic model of a prey and predator planktonic species. The positivity and boundedness of the solution are studied. The possible equilibriums and their local stability are analyzed; also the global stability of the system around the interior equilibrium is established. We examine the optimal harvesting policy to discuss the dynamical profit of the interacting planktonic species. To show the impact of the toxicity coefficient, we have made analytical estimates that are validated using simulations. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical model with delay which describes the dynamics of three fish populations. The equilibrium points and their stability properties of the non-delay model are studied using Eigenvalue analysis. For the system with single delay model and multiple delays model, the existence of the interior equilibrium point and its stability are studied using the characteristic equation for the linearized system. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model consisting of three populations with discrete time delays is considered. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of Hopf bifurcations at the coexistence equilibrium is established. The direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are analyzed using the theory of normal form and center manifold. Discussion with some numerical simulation examples is given to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we present an efficient fifth-order method for solving the standard linear optimization problems. In order to do this, we show that solving this problem is equivalent to solving a system of nonlinear equations. Therefore, we build a sequence of functions giving an approximate solution of this system. To find this approximation, we give an algorithm, which is based on the idea of the Sharma's method. Computational efficiency, in its general form, is discussed, and a comparison between the efficiency of proposed technique and existing one is made. The performance is tested through numerical examples. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the examples. [ABSTRACT FROM AUTHOR]