Plankton Models and Its Attractors in a Local Approximation

Abstract

The previously accepted models of plankton consisting of two interacting populations—phytoplankton and zooplankton—are considered in a local approximation. The analysis of models is carried out with the help of a qualitative study of systems of differential equations as a whole (i.e., in the entire phase space of systems, not limited to a neighborhood of equilibrium positions). Analytical conditions for the occurrence of a Hopf bifurcation are obtained for each model using the Lyapunov stability theory. A comparison of various models is given, and their shortcomings associated with the incompleteness of research are indicated. It has been established that in some cases the loss of stability of the equilibrium position does not lead to the formation of a limit cycle (Hopf bifurcation) but to the formation of a limit continuum with a chaotic behavior of the trajectories in a large part of the phase space. It is shown that the parameters significantly influencing the dynamics of the development of plankton are the natural mortality of populations as an environmental characteristic of the environment.