Strategies for ensuring functional stability of a complex sensor network based on the research of the dynamics of the behavior of evolutionary equations

Wireless sensor networks play an increasingly important role in navigation and monitoring tasks in modern conflict environments, where their operation is continuously affected by destabilizing external and internal factors. Ensuring the functional stability of such networks under sustained adverse influence therefore represents a critical scientific and practical problem. This paper develops a mathematically grounded framework for analyzing and maintaining the functional stability of a complex wireless sensor network operating under risk exposure. The qualitative theory of differential equations is applied to describe and characterize the state of the system under such conditions. To mathematically formalize the behavior of the sensor network, the classical evolutionary SIR model is employed, and constructive conditions for network stability and asymptotic stability are formulated. Three functional stability strategies – constant monitoring, impulsive recovery, and periodic recovery – are formally introduced and analyzed within a unified modeling framework. For each strategy, explicit conditions are obtained under which the number of compromised network nodes asymptotically decreases, ensuring the preservation of network functionality. The effects of recovery and restoration actions are analyzed using phase-plane methods. The dependence of network stability on model parameters describing node compromise, attrition, and recovery rates is established, and an analytical model for determining the time required to restore functional stability is derived. The resulting mathematical framework provides a rigorous theoretical basis for selecting and comparing functional stability strategies for wireless sensor networks operating under persistent destabilizing conditions.