A Three‐Species Model With Predator‐Taxis Sensitivity: Hopf Bifurcation and Active Control Stabilization

ABSTRACT This study presents an analysis of a novel fractional two prey–one predator model incorporating predator‐taxis sensitivity. We conduct a comprehensive stability analysis, explore the model's chaotic nature through period‐doubling bifurcations, and also show the existence of limit cycles through fractional Hopf bifurcation. It is observed that the fractional‐order parameter brings in a stabilizing effect and, simultaneously, a shift of the Hopf bifurcation point. At the Hopf bifurcation point, the system moves from stable equilibria to sustained oscillations. In addition, regardless of initial conditions, the system approaches a stable limit cycle, showing the robustness of the method. We also demonstrate the effectiveness of the active control method to eliminate the periodicity of the fractional system and also unravel the decelerating influence of the fractional‐order parameter on the convergence time to equilibrium. These results provide valuable insights into the stabilization of ecosystem dynamics and contribute more broadly to our understanding of population dynamics in ecological systems.