Dynamics, bifurcation, and chaos control in a fractional-order discrete multi-team predator–prey model

In this paper, a discrete-time fractional-order multi-team predator–prey model derived from a Caputo-type fractional framework was proposed and analyzed. The model describes the nonlinear interactions between two cooperating prey populations and a common predator species, where the fractional-order parameter modulates the influence of past states through the fractional discrete formulation. An algebraic stability criterion based on the characteristic polynomial coefficients of the Jacobian matrix was employed to investigate the local asymptotic stability of the coexistence equilibrium without relying on explicit eigenvalue computations. The necessary and sufficient analytical conditions for the occurrence of flip and Neimark–Sacker (NS) bifurcations were derived, and the associated codimension-two flip–NS bifurcation was rigorously characterized. Numerical simulations validated the theoretical results and revealed complex dynamical behaviors, including periodic oscillations, quasiperiodicity, and chaos. To suppress unstable oscillations, three chaos control strategies—Ott–Grebogi–Yorke (OGY) feedback control, hybrid control, and state feedback control—were implemented. A systematic quantitative comparison based on convergence speed, control effort, and stabilization robustness was conducted to evaluate their relative performance and to clarify their ecological management implications. The results showed that the fractional-order parameter significantly affects stability thresholds and bifurcation organization, thereby reshaping the qualitative structure of population dynamics. These findings highlight the regulatory role of fractional-order effects in discrete ecological systems and provide a rigorous framework for stability analysis and controlled ecosystem management.