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Structural stability analysis of an algal bloom mathematical model in tropic interaction. (English) Zbl 1201.34072
Summary: The paper deals with the dynamical behavior of a plankton population ecosystem. The ecosystem is represented by a set of two dimensional non-linear differential equations. We propose a description as an excitable system which resembles the behavior of excitable media. We have analyzed the stability and bifurcation of the model system with and without delay. We have shown the existence and uniqueness of limit cycles in the rapid growth of the plankton population. We also study the model system as a stochastic one, by incorporating random fluctuations of the environment. And we study the stochastic stability of the dynamical system in mean square sense around the interior equilibrium.
MSC:
34C60Qualitative investigation and simulation of models (ODE)
34K60Qualitative investigation and simulation of models
34C05Location of integral curves, singular points, limit cycles (ODE)
34D20Stability of ODE
34C23Bifurcation (ODE)
34F05ODE with randomness
92D40Ecology