Delayed Hopf Bifurcation and Space–Time Buffer Curves in the Complex Ginzburg–Landau Equation

• Published in: IMA journal of applied mathematics Vol. 87; no. 2; pp. 131 - 186
• Main Authors: Goh, Ryan, Kaper, Tasso J, Vo, Theodore
• Format: Journal Article
• Language: English
• Published: Oxford University Press 12.04.2022
• Subjects: dynamic bifurcation in PDEs; stationary phase method; reaction–diffusion equations; complex Ginzburg–Landau equation; slow passage through Hopf bifurcation; spatially inhomogeneous onset of oscillations; hard onset of oscillations; steepest descents method

Abstract In this article, the recently discovered phenomenon of delayed Hopf bifurcations (DHB) in reaction–diffusion partial differential equations (PDEs) is analysed in the cubic Complex Ginzburg–Landau equation, as an equation in its own right, with a slowly varying parameter. We begin by using t...