International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3738 2020 2020 Department of Mathematics, Faculty of Science, Al-Baha University, Albaha 65525, Saudi Arabia; Academy of Engineering and Medical Sciences, Department of Mathematics, Khartoum, Sudan Thwiba Thwiba The study examines the dynamics of a predator-prey model that includes temporal delays, concentrating on the impact of these delays on system stability and behavior.It delineates criteria for the global stability of the positive equilibrium using a generalized Lyapunov function and the Razumkin-type theorem, emphasizing the significance of temporal delays in biological systems. The research highlights the Neymark-Saker (NS) bifurcation, examining the impact of fractional configurations on this bifurcation and the system’s overall dynamic stability. The research utilizes the Lyapunov-Razumihin approach to identify bifurcation points and forecast the system’s progression in intricate ecological settings. The research examines the presence of periodic solutions and local stability criteria related to the two delays in predator-prey interactions. Numerical simulations are used to substantiate the theoretical results, specifically for the periodic bifurcation solutions associated with the Neymark-Saker bifurcation. 2025 2025 310 323 10.54216/IJNS.260224 https://www.americaspg.com/articleinfo/21/show/3738