Lagrangian descriptors for stochastic differential equations: a tool for revealing the phase portrait of stochastic dynamical systems

Francisco Balibrea Iniesta, Carlos Lopesino, Stephen R Wiggins, Ana M Mancho

Research output: Contribution to journalArticle (Academic Journal)

9 Citations (Scopus)
261 Downloads (Pure)

Abstract

In this paper we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of Lagrangian descriptors to stochastic differential equations. Analogously to the deterministic differential equations setting, the Lagrangian descriptors graphically provide the distinguished trajectories and hyperbolic structures arising within the stochastic dynamics, such as random fixed points and their stable and unstable manifolds. We analyze the sense in which structures form barriers to transport in stochastic systems. We apply the method to several benchmark examples where the deterministic phase space structures are well-understood. In particular, we apply our method to the noisy saddle, the stochastically forced Duffing equation, and the stochastic double gyre model that is a bench-mark for analyzing fluid transport.
Original languageEnglish
Article number1630036
Number of pages20
JournalInternational Journal of Bifurcation and Chaos
Volume26
DOIs
Publication statusPublished - 15 Dec 2016

Keywords

  • Stochastic differential equation
  • Lagrangian descriptor
  • distinguished trajectories
  • hyperbolicity
  • random fixed point
  • stable and unstable manifolds

Fingerprint Dive into the research topics of 'Lagrangian descriptors for stochastic differential equations: a tool for revealing the phase portrait of stochastic dynamical systems'. Together they form a unique fingerprint.

Cite this