Conditioned Lyapunov exponents for random dynamical systems
| Autor: | Jeroen S. W. Lamb, Martin Rasmussen, Maximilian Engel |
|---|---|
| Přispěvatelé: | Engineering & Physical Science Research Council (EPSRC), Commission of the European Communities |
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
Context (language use) Dynamical Systems (math.DS) Lyapunov exponent 01 natural sciences Stability (probability) 0101 Pure Mathematics symbols.namesake Stochastic differential equation QUASI-STATIONARY DISTRIBUTIONS 0102 Applied Mathematics Attractor FOS: Mathematics Applied mathematics Mathematics - Dynamical Systems 0101 mathematics Mathematics Hopf bifurcation ATTRACTORS Science & Technology Stochastic process Applied Mathematics 010102 general mathematics Bounded function Physical Sciences 37A50 37H10 37H15 60F99 symbols HOPF-BIFURCATION math.DS |
| Zdroj: | Transactions of the American Mathematical Society. 372:6343-6370 |
| ISSN: | 1088-6850 0002-9947 |
| Popis: | We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to tra-jectories that stay within a bounded domain for asymptotically long times. This is motivated by thedesire to characterize local dynamical properties in the presence of unbounded noise (when almost alltrajectories are unbounded). We illustrate its use in the analysis of local bifurcations in this context.The theory of conditioned Lyapunov exponents of stochastic differential equations builds on thestochastic analysis of quasi-stationary distributions for killed processes and associated quasi-ergodic dis-tributions. We show that conditioned Lyapunov exponents describe the asymptotic stability behaviourof trajectories that remain within a bounded domain and – in particular – that negative conditionedLyapunov exponents imply local synchronisation. Furthermore, a conditioned dichotomy spectrum isintroduced and its main characteristics are established. |
| Databáze: | OpenAIRE |
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