Dynamic analysis and optimal control of a fractional order predator-prey model with economic threshold

In this paper, a fractional order differential algebraic predator-prey system with Holling type functional response was presented. The dynamic behavior of populations under the influence of economic benefits was thoroughly investigated. Specifically, with economic benefit as the bifurcation parameter, the existence of singularity-induced bifurcation was analyzed based on the theory of differential algebraic system. After that, a state feedback controller was designed to eliminate the singularity induced bifurcation and stabilize the system near the corresponding interior equilibrium. Furthermore, an optimal control problem was formulated, and the necessary conditions were derived. In addition, the validity of the theoretical results was confirmed through extensive numerical simulations.