4.3 Lyapunov Exponent – The Chaos Hypertextbook

The Lyapunov exponent is a number that measures stability. In this page, the Lyapunov exponent is applied to an equation that jumps between stability and instability, between chaos and order — the logistic equation.

4.3 Lyapunov Exponent Standard map orbits rendered with Std Map . Descriptions of the sort given at the end of the prevous page are unnatural and clumsy. It would be nice to have a simple measure that could discriminate among the types of orbits in the same manner as the parameters of the harmonic oscillator. Consider two points in a space, X 0 and X 0 + Δx 0 , each of which will generate an orbit in that space using some equation or system of equations. These orbits can be thought of as parametric functions of a variable that is something like time. If we use one of the orbits a referen

related reading

• Chaos and Randomnessblog.evjang.com
• Lyapunov time - Wikipediam.wikipedia.org
• Stochastic Stability of Differential Equationslink.springer.com
• 8. System resilience — Computational aging bookcomputationalaginglab.github.io
• 1.2: The Logistic Equation - Mathematics LibreTextsmath.libretexts.org
• Chaos theory - Wikipediaen.wikipedia.org
• Chaos is not rare in natural ecosystems | Nature Ecology & Evolutionnature.com
• Shtetl-Optimized >> Blog Archive >> The First Law of Complexodynamicsscottaaronson.blog
• The Concentration of Invariant Measures for Stochastic Dynamical Systems with Locally Lipschitz Continuous Coefficients in R^darxiv.org
• Power law - Wikipediaen.wikipedia.org
• Lipschitz continuityen.wikipedia.org
• Chaos Theory and Fractalstnellen.com