Research Information System
1st lnternational Conference on Mathematics and Applied Data Science, Konya, Turkey, 29 - 31 August 2025, no.440, pp.175, (Summary Text)
Mathematical modeling is imperative for comprehending the nonlinear and temporally structured interactions that govern marine ecosystems. In regions where fishing pressure is high or environmental sensitivity is a concern, such as the Black Sea, the application of these models is of particular importance. These models play a crucial role in predicting long-term species dynamics and evaluating the sustainability of fisheries management strategies [1]. A delay differential equation (DDE) framework provides a transparent yet powerful structure that links biological realism with mathematical tractability. In this study, a biologically informed DDE model is developed to investigate the trophic interactions among four ecologically and economically important marine fish species in the Black Sea: the anchovy, horse mackerel, bluefish and Atlantic bonito. The model incorporates species-specific time delays corresponding to reproduction, predation and other ecological processes. The temporal discrepancies have been determined through the analysis of empirical literature and ecological data. These delays are indicative of biologically realistic lags in spawning cycles, feeding behavior and growth dynamics, thereby facilitating a more accurate depiction of seasonal and interannual biomass fluctuations. A comprehensive analytical investigation was conducted, encompassing equilibrium analysis and local stability assessment. The present investigation employed the characteristic equations of the DDE system to facilitate a comprehensive evaluation. The implementation of bifurcation analysis enables the discernment of critical thresholds in predation rates and delay parameters, where Hopf bifurcations emerge, giving rise to oscillatory dynamics [2]. These findings underscore the pivotal role of time delays in the destabilization of steady-state coexistence, thereby giving rise to biologically meaningful population cycles. The execution of numerical simulations is facilitated by the MATLAB dde23 solver. The results obtained demonstrate the efficacy of emphasizing the significance of delay effects in elucidating the dynamics of predator–prey interactions. Sensitivity analysis further reveals the dominant influence of bonito assimilation and bluefish predation on system variability. This modeling approach supports ecosystem-based fishery management by providing biologically grounded and computationally reliable insights into long-term fish population dynamics.