## 3 Mathematical Model of Radar Operation Under Interference Conditions  
To develop a mathematical model for radar operation under jamming conditions, the GERT network modeling approach was selected. GERT (Graphical Evaluation and Review Technique) network is a probabilistic modeling tool used to analyze systems with complex dependencies. Unlike traditional network methods, GERT allows for probabilistic transitions and time delays. This makes it particularly valuable for studying processes with uncertainty, such as radar operation under interference conditions [12; 13; 14]. Several key advantages support the choice of this modeling technology:  
1. Comprehensive representation of complex processes. During radar operation under jamming conditions, it is essential to account for all possible factors such as search, acquisition, tracking, and target transmission. Each of these stages can be affected by various failures or delays due to jamming. The GERT network allows for the visualization and formalization of these complex processes, incorporating probabilistic dependencies and time characteristics. Analysis of various jamming scenarios. The GERT network enables the visualization and analysis of different jamming scenarios, including their occurrence probabilities and jamming intensities. 3. Time delays and their impact on system performance. GERT modeling accounts for the time characteristics of processes, allowing for the formalization of delays caused by jamming. This is particularly important for understanding how delays at different stages (search, acquisition, tracking) impact overall radar performance. Such insights are vital for optimizing system timing parameters. 4. Identification and analysis of critical paths. Under jamming conditions, it is crucial to identify critical paths where significant delays or disruptions might occur. The GERT network helps pinpoint and analyze these paths, aiding in the development of strategies to minimize or eliminate operational delays, ensuring better planning and protection at the design stage. 5. Visualization of processes and results. The GERT network provides a graphical representation of processes, making it easier to understand the radar's structure and behavior in jamming conditions. This enhances communication and analysis during the design and operational phases. In summary, using the GERT network modeling approach for developing a radar operation model under jamming conditions offers a comprehensive way to incorporate probabilistic and time characteristics and to analyze jamming scenarios. These benefits highlight the potential of GERT modeling in addressing radar operation under challenging jamming environments. Incorporating new jamming factors into mathematical models of radar systems represents a relevant and complex challenge that requires balancing increased model complexity with the need to maintain its reliability and computational efficiency. Jamming factors can include both natural sources of interference, such as atmospheric noise, and artificial ones, such as coordinated radar attacks and deceptive jamming techniques. The proposed model addresses this challenge using several approaches. Firstly, each type of jamming is modeled using probabilistic distributions that reflect its temporal and spatial properties. For instance, noise jamming is represented by Gaussian distributions, while deceptive jamming may require the application of non-Gaussian or multimodal distributions. Such flexibility in modeling distributions is achieved through the use of GERT (Graphical Evaluation and Review Technique) modeling technology. Secondly, a multi-layered modeling approach is applied, where the effects of interference are divided into distinct levels, such as noise, signal distortion, and false target generation. This allows the impact of each factor to be isolated and adjusted independently, without disrupting the overall system. Moreover, the reliability of the model is assessed through iterative simulations in which the intensity and type of jamming are varied.