Bifurcation of quantum electron-acoustic waves (QEAWs) is studied in an adiabatic quantum plasma with nonextensively distributed hot electrons. Using reductive perturbation technique, modified Kortweg de Vries (KdV) equation is derived with dual power nonlinearity for highly nonlinear QEAWs. Using Galilean transformation the modified KdV equation is reduced to a planar dynamical system with three equilibrium points. Applying phase plane analysis periodic wave solutions and supernonlinear periodic wave solutions for QEAWs are perceived. It is found that the amplitude of the nonlinear structures is indirectly proportional to the ratio of number densities (μ), the cold to hot electron temperature ratio (σ) and the nonextensivity parameter (q), we have explained physically that confronts our results. In addition, coexistence of superperiodic and quasiperiodic phenomena, quasiperiodic and chaotic phenomena and chaotic, superperiodic and quasiperiodic phenomena for QEAWs are observed for appropriate initial values.
