Oran bağimli av-avci modelinin korku ve siğinmaetki̇si̇yle bi̇rli̇kte kararliliği ve yakinsakliği

This study investigates ratio-dependent predator--prey models incorporating fear effects and prey refuge mechanisms to better understand ecosystem dynamics. Starting from Leslie's ratio-dependent formulation, extended models are constructed by introducing behavioral responses and refuge effects. The existence and local stability of the interior equilibrium are analyzed using Jacobian matrix techniques. Numerical simulations support the theoretical results and illustrate how fear and refuge mechanisms influence transient dynamics while preserving long-term coexistence. The results indicate that these mechanisms act as stabilizing buffers that enhance the biological realism of predator--prey interactions without destabilizing the system.