dorsal/arxiv
View SchemaLyapunov exponents in constrained and unconstrained ordinary differential equations
| Authors | Michael D. Hartl |
|---|---|
| Categories | |
| ArXiv ID | physics/0303077 |
| URL | https://arxiv.org/abs/physics/0303077 |
Abstract
We discuss several numerical methods for calculating Lyapunov exponents (a quantitative measure of chaos) in systems of ordinary differential equations. We pay particular attention to constrained systems, and we introduce a variety of techniques to address the complications introduced by constraints. For all cases considered, we develop both deviation vector methods, which follow the time-evolution of the difference between two nearby trajectories, and Jacobian methods, which use the Jacobian matrix to determine the true local behavior of the system. We also assess the merits of the various methods, and discuss assorted subtleties and potential sources of error.
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"abstract": "We discuss several numerical methods for calculating Lyapunov exponents (a\nquantitative measure of chaos) in systems of ordinary differential equations.\nWe pay particular attention to constrained systems, and we introduce a variety\nof techniques to address the complications introduced by constraints. For all\ncases considered, we develop both deviation vector methods, which follow the\ntime-evolution of the difference between two nearby trajectories, and Jacobian\nmethods, which use the Jacobian matrix to determine the true local behavior of\nthe system. We also assess the merits of the various methods, and discuss\nassorted subtleties and potential sources of error.",
"arxiv_id": "physics/0303077",
"authors": [
"Michael D. Hartl"
],
"categories": [
"physics.comp-ph"
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"title": "Lyapunov exponents in constrained and unconstrained ordinary differential equations",
"url": "https://arxiv.org/abs/physics/0303077"
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