In this paper, a discrete periodic predator–prey system with type IV functional responses and time delay is investigated. Using Gaines and Mawhin’s continuation theorem from coincidence degree theory as well as some prior estimates, we get sufficient conditions for the existence of positive periodic solutions of the system. This is also the first time that the coincidence degree theory has been used to obtain multiple positive periodic solutions in discrete ecological systems.

Electro-hydrostatic actuator (EHA) has significance in a variety of industrial tasks. For the purpose of elevating the working performance, we put forward a sliding mode control strategy for EHA operation with a damping variable sliding surface. To start with, a novel sliding mode controller and an extended state observer (ESO) are established to perform the proposed control strategy. Furthermore, based on the modeling of the EHA, simulations are carried out to analyze the working properties of the controller. More importantly, experiments are conducted for performance evaluation based on the simulation results. In comparison to the widely used control strategies, the experimental results establish strong evidence of both overshoot suppression and system rapidity.