| Predatory fishing optimization model has been concerned and studied byscholars and researchers all around the world$.$Based on the previous work offishing optimization model, combining the actual situation, this paper puts forward afishery resource system-based dynamic model: it possesses twoaquatic environments-protecting area (fishing prohibiting) and non-protectingarea (fishing allowing), meanwhile it has a stage-structure, which means predatorsare divided into two types: juvenile and adult predators. With Routh-HurwitzCriterion and mechanical theorem proving, we analysis the local stability of thesystem, and use proper Lyapunov function to analysis the global stability of thesystem. In addition, the article also utilizes Pontryagin Maximum Principle to obtainmathematical formulae of optimal fishing strategy.This paper discuss monotonicity and stability of the characteristicpolynomial of the autoregressive transfer function of system. Moreover, the articledefines auxiliary function according to correlated conditions for stability of theHurwitz polynomial. Then it combines symbolic computation of math software todiscuss the scope of the control parameters, and followed with the qualitative andquantitative analysis. It is possible to adjust the systematic overshoot and responsetime and make the system to meet preferable performance. |
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