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Bifurcations in a delayed differential-algebraic plankton economic system
Keywords:Differential-algebraic equations; Harvesting; Delay; Stability switches; Singularity-induced bifurcation.
Abstract:
      This paper considers a phytoplankton-zooplankton bio-economic system with delay and harvesting, which is described by differential-algebraic equations. Local stability analysis of the system without delay reveals that a singularity-induced bifurcation phenomenon appears when a variation of the economic interest is taken into account, furthermore, a state feedback controller is designed to stabilize the system at the interior equilibrium. Then, we show that delay, which is considered in the toxic liberation, can induce stability switches, such that the positive equilibrium switches from stability to instability, to stability again and so on. Finally, some numerical simulations are performed to justify analytical findings.