A manifold independent approach to understanding transport in stochastic dynamical systems

DOI10.1016/S0167-2789(02)00659-0zbMath1008.37021OpenAlexW2092683308MaRDI QIDQ1848742

Lora Billings, Erik M. Bollt, Ira B. Schwartz

Publication date: 13 November 2002

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(02)00659-0

zbMATH Keywords

noiseFrobenius-Perron operatorepidemiologybi-stabilitymeaslesstochastic bifurcationheteroclinic tanglestochastic chaostwo-attractor system

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Discrete-time control/observation systems (93C55) Operator-theoretic methods (93B28) Ergodic theorems, spectral theory, Markov operators (37A30) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Random dynamical systems (37H99)

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Cites Work

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• Infinite subharmonic bifurcation in an SEIR epidemic model
• Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models
• All invariant densities of piecewise linear Markov maps are piecewise constant
• Approximating measures invariant under higher-dimensional chaotic transformations
• Chaotic transport in dynamical systems
• Small amplitude, long period outbreaks in seasonally driven epidemics
• Finite approximation for the Frobenius-Perron operator. A solution to Ulam's conjecture
• Chaos, fractals, and noise: Stochastic aspects of dynamics.
• Bi-instability and the global role of unstable resonant orbits in a driven laser
• Estimating statistics of neuronal dynamics via Markov chains
• Exciting chaos with noise: unexpected dynamics in epidemic outbreaks
• The projection method for computing multidimensional absolutely continuous invariant measures
• An analytical study of transport in Stokes flows exhibiting large-scale chaos in the eccentric journal bearing
• Stability of dynamical systems
• Approximating physical invariant measures of mixing dynamical systems in higher dimensions
• Melnikov Process for Stochastically Perturbed, Slowly Varying Oscillators: Application to a Model of Wind-Driven Coastal Currents
• Piecewise linear markov approximations of frobenius-perron operators associated with multi-dimensional transformations

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