This paper describes the dynamic interaction between plasmons in a two dimensional electron gas system under electrical tuning to the high density regime in AlN/GaN high electron mobility transistor. The results demonstrate an enhanced resonance when the two plasmons are commonly excited, during which the potentially splitting phenomenon of such resonance is explored in detail. An asymmetrical plasmon possess wide frequency tunability has also been demonstrated in the AlN/GaN system, on the contrary, the results also indicate a finite tunable regime of symmetrical-plasmons as limited by the coupling strength between such plasmons. For the devices with narrow gate-fingers, significant near-field enhancement can be obtained due to the strong cavity pumping of electromagnetic energy. These properties may have important applications including high-responsivity quantum-dot detection systems, THz modulator etc.