Transition to chaos in high control parameter of Swift–Hohenberg equation

Abstract

The Swift-Hohenberg equation, which is a parabolic equation, is studied at high values of the control parameter. The method used is exponential time differencing combined with fourth-order Runge-Kutta (ETDRK4). The solution obtained was subjected to spectral analysis. In the case of real equations, it can be shown that there is a transition from regular to chaotic dynamics at the control parameter of 23.6. Meanwhile, in the case of equations with complex terms, transition to chaotic dynamics occurs at low control parameter and the imaginary constant range of −8 ≤ b ≤ −6. It can be concluded that the Swift-Hohenberg equation can produce chaotic dynamics at certain parameter values.