The nonlinear dynamics of wave turbulence in a dissipative magnetized plasma system, comprised hot electrons and cold ions, are investigated using the hydrodynamical type of nonlinearity. The temporal dynamics, as well as the existence of stable and unstable cycles in the phase space, are examined through the three-wave and four-wave couplings. In three-mode model, the behavior of the system comprised of periodic motion, unstable modulated multiperiodic motions and stochastic motions depending on the linear frequency mismatches. In the four-mode model, two coupled wave-triplets behave similarly, and chaos occurs with a growth rate higher than the three-mode coupling. With the detuning effect, the system displays coexisting non-chaotic and chaotic regions. In this case, all cycles are deformed so that the coupled states fill the stable and unstable manifolds describing the appearance of islands (soliton-like solutions). The time evolution of the Hamiltonian-like function shows two regimes of mode saturation observed in the interaction of wave modes and energetic particles. This scenario maintains an energy-like function and then identifies the conservative invariant manifolds in the dissipative nonlinear mode-coupling of both models.