Controlling population oscillations in a delayed Lotka-Volterra model with Z-type control

Abstract

The current study proposes and analyses a delayed predator-prey model with Z-type control. We adopted the modified Lotka-Volterra (LV) model to take into consideration for gestation delay in predator population growth. The proposed model's core mathematical properties are investigated using equilibrium analysis, stability analysis, and bifurcation theory. The modified LV model's coexistence equilibrium is well proven as being globally asymptotically. However, we have found that delay can destabilise the system by producing limit cycle oscillations. We also discover that if the indirect Z-controller is applied in the predator population, population oscillations may be eradicated. The resulting oscillations can be replaced by new stable steady state or limit cycle oscillations with different magnitudes. We conduct comprehensive computational experiments to investigate the system's global dynamics as well as the potential applications of the Z-type control mechanism.