Nonlinear stability and chaos in electrohydrodynamics (Q1772661)

The nonlinear stability of two superposed dielectric fluids is investigated using the method of multiple scales. The critical electric field for the linear instability condition is found to be independent of viscosity and the variable gravity parameter. For the nonlinear problem, a generalized equation governing the evolution of the amplitude is derived in marginally unstable regions of parameter space and the solutions are obtained both analytically and numerically. The method of generalized synchronization is used to obtain the equations describing the modulation of the amplitude and phase. Lyapunov's first method is used to find the stability of the proposed solution. Numerical solutions are presented giving the effects of different parameters on the stability, response and chaos.