Fractional Nonlinear Rogue-Wave Modeling, Stability Analysis, and Optimal Control of Insecurity Dynamics in South–South Nigeria

Insecurity in South–South Nigeria exhibits sudden and extreme escalation patterns that resemble rogue-wave phenomena in nonlinear dynamical systems. This study proposes a nonlinear rogue-wave mathematical model to describe insecurity outbreaks and investigates their stability properties and optimal control mechanisms. A modified nonlinear Schrödinger–type framework is employed to capture amplification, dispersion, and external socio-economic influences driving insecurity surges. Analytical results establish conditions for existence and stability, while rogue-wave emergence explains abrupt insecurity spikes. An optimal control problem incorporating non-kinetic intervention strategies is formulated and solved using Pontryagin’s Maximum Principle. Numerical simulations demonstrate that appropriately timed controls significantly suppress extreme insecurity events. The model provides a rigorous theoretical foundation for understanding insecurity dynamics and supports the design of effective, proactive security policies for South–South Nigeria.

Keywords: Rogue wave, Insecurity dynamics, optimal control, nonlinear systems, Stability analysis.