| Abstract: |
| This work investigates the discrete-time dynamics of a predator--prey model incorporating a square root functional response, fear effect, and immigration. Using bifurcation theory and center manifold analysis, the study establishes the occurrence of period-doubling and Neimark--Sacker bifurcations in the positive quadrant. Numerical simulations support the analytical results and illustrate complex behaviors such as high-period orbits, quasi-periodic invariant curves, and chaotic attractors. To control chaotic dynamics, both the Ott--Grebogi--Yorke technique and a state-feedback control method are applied, showing that the system can be guided toward a stable equilibrium. The results provide useful insight into the dynamics and control of nonlinear ecological systems. |
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