Panda, N.

Adaptive control of synchrony in neuronal networks is central to understanding both normal brain function and pathological states such as epilepsy and tremor. We study a modified FitzHugh-Nagumo (FHN) network in which the local excitability is extended by a fifth-order nonlinearity and the global coupling strength adapts homeostatically to the spatial variance of neural activity. Using a combination of numerical bifurcation analysis and direct time-domain simulation, we map regimes of quiescence, stable fixed point, and self-sustained oscillation in the two-parameter space of input current and nonlinearity. The analytically predicted Hopf boundary agrees closely with the simulated transition to oscillations. Extending to networks with ring, Watts-Strogatz, and Barabasi-Albert topologies, we show that variance-driven adaptation strongly increases coupling and synchrony in rings, is partly suppressed in small-world graphs, and is almost ineffective in scale-free networks where hubs dominate connectivity. A simple feedback controller regulating the Kuramoto order parameter enables targeted desynchronization or resynchronization. Finally, stochastic forcing produces a non-monotonic impact on coherence, suggesting noise-induced resonance effects. This simulation-based framework links single-neuron excitability, network topology, and adaptive coupling control, and may inform strategies for brain-computer interfaces and neuromodulation therapies.