Bifurcation analysis of a singular nutrient-plankton-fish model with taxation, protected zone and multiple delays. (English) Zbl 1478.92247
Summary: A differential algebraic nutrient-plankton-fish model with taxation, free fishing zone, protected zone and multiple delays is investigated in this paper. First, the conditions of existence and control of singularity induced bifurcation are given by regarding economic interest as bifurcation parameter. Meanwhile, the existence of Hopf bifurcations are investigated when migration rates, taxation and the cost per unit harvest are taken as bifurcation parameters respectively. Next, the local stability of the interior equilibrium, existence and properties of Hopf bifurcation are discussed in the different cases of five delays. Furthermore, the optimal tax policy is obtained by using Pontryagin’s maximum principle. Finally, some numerical simulations are presented to demonstrate analytical results.
MSC:
| 92D40 | Ecology |
| 34A09 | Implicit ordinary differential equations, differential-algebraic equations |
| 91B76 | Environmental economics (natural resource models, harvesting, pollution, etc.) |
| 34H05 | Control problems involving ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
Keywords:
nutrient-plankton-fish model; free fishing zone; taxation; singularity induced bifurcation; Hopf bifurcation; Pontryagin’s maximum principleReferences:
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