Bifurcation analysis and control of a class of hybrid biologicaleconomic models

摘要

This paper systematically studies a hybrid predator-prey economic model, which isformulated by differential-difference-algebraic equations. It shows that this model exhibitstwo bifurcation phenomena at the intersampling instants. One is saddle-node bifurcation,and the other is singular induced bifurcation which indicates that economic profit maybring impulse at some critical value, i.e., rapid expansion of biological population interms of ecological implications. On the other hand, for the sampling instants, the systemundergoes Neimark-Sacker bifurcation at a critical value of economic profit, i.e., theincrease of economic profit destabilizes the system and generates a unique closed invariantcurve. Moreover, the state feedback controller is designed so that singular inducedbifurcation and Neimark-Sacker bifurcation can be eliminated and the population can bedriven to steady states by adjusting harvesting costs and the economic profit. At the sametime, by using Matlab software, numerical simulations illustrate the effectiveness of theresults obtained here.