Abstract
•The nonlinear Schrödinger equation studied by bifurcation dynamical system.•The bifurcation analysis modulated the physical stable solutions.•Electron superthermality affected the envelope, periodic and shock characteristics.•The results are important in strong dispersion mesospheric dusty plasmas.
The bifurcation and dynamical system (BDS) investigation have been applied to study the nonlinear Schrödinger equation (NLSE) in strong dispersive dusty plasmas model contains three fluid of negative-positive grains and ion components with superthermal electron. For a stable regime, the parameters of superthermal index (κ) of electron, negative or positive dust densities (NDn) and(NDp) effects on the dust-ion envelope, periodic, shock forms are scrutinized. It is value noted that the outcomes presented here could be usable in the mesospheric space applications.