Pitchfork bifurcation along a slow parameter ramp: Coherent structures in the critical scaling

Studies in Applied Mathematics, Journal Year: 2024, Volume and Issue: 153(2)

Published: May 11, 2024

Abstract We investigate the slow passage through a pitchfork bifurcation in spatially extended system, when onset of instability is slowly varying space. focus here on critical parameter scaling, locus propagates with speed , where small that measures gradient ramp. Our results establish how mediated by front traveling ramp, and demonstrate scalings for delay or advance relative to depending sign direction propagation ramp bifurcation. The also include generalization classical Hastings–McLeod solution Painlevé‐II equation equations drift term.

Language: Английский

Delayed loss of stability of periodic travelling waves: Insights from the analysis of essential spectra

Journal of Theoretical Biology, Journal Year: 2024, Volume and Issue: unknown, P. 111945 - 111945

Published: Sept. 1, 2024

Language: Английский