Abstract

To describe adolescent violence within the interrelated parent-child triangular system, the research offers a network technique for building a biomathematical framework. Rather than viewing adolescent violence as a single outcome, the study treats it as a state variable in a networked system, with other state variables connected by a directed, weighted graph. Combining network topology with dynamical systems thinking for non-linearity is a methodological innovation that makes it possible to examine structural connectivity alongside temporal dynamics, equilibria, stability, and susceptibility to perturbations. Sensitivity analysis evaluates how sensitive the system paths are to changes in state and parameters, whereas centrality measures identify structurally significant nodes. This method distinguishes dampening from reinforcing connections, yielding a mathematically comprehensible definition of the variety of family ties. In contrast to earlier association-based approaches, the integrated framework accounts for how minor adjustments at the local relationship level can affect the entire family system. This standard model can identify the main nodes that dynamically affect the system, both statistically and computationally.