Lecture 12 basic lyapunov theory stanford university. The synchronization of electrical activity in the brain occurs as the result of interaction among sets of. Pronunciation of lyapunov with 1 audio pronunciation, 1 synonym, 6 translations and more for lyapunov. Let v x,t be a nonnegative function with derivative v. A second technique consists in using the lyapunovfloquet transformation to re cast a linear timeperiodic system in a timeinvariant one 37, 38. Lyapunov exponent tags are words are used to describe and categorize your content. Our company is reckoned among the top 10 ip firms by electronic filings in. Based on a lyapunov function, this paper proves the stability of implicit selftuning controllers, combining recursive parameters estimation with a forgetting factor and generalized minimum variance criterion, for timevarying systems.
Calculation lyapunov exponents for ode file exchange. Finding lyapunov functions1 this lecture gives an introduction into basic methods for. Find lyapunov function for each of the attractive fixed points. Wolf et al determining lyapunov exponents from a time series 287 the sum of the first j exponents is defined by the long term exponential growth rate of a jvolume element. The alogrithm employed in this m file for determining lyapunov exponents was proposed in a. This alternate definition will provide the basis of our spectral technique for experimental data. The real building blocks of the universe with david tong duration. Dans le cas particulier des systemes lineaires invariants dans le temps lti secrivant. R n is an equilibrium point of the system if fxe 0 xe is an equilibrium point xt xe is a trajectory suppose xe is an equilibrium point system is globally asymptotically stable g. This matlab function solves the special and general forms of the lyapunov equation. The system parameters are considered to be changing continuously but slowly or changing abruptly but infrequently. Vastano, determining lyapunov exponents from a time series, physica d, vol. Combine multiple words with dashes, and seperate tags with spaces.
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