Predicting the outcome of a chaotic system using lyapunov exponents
AssigneeU.S. Government as represented by the Secretary of the Army
InventorsGORDEN VIDEEN, ROBERT H. DALLING
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Abstract
Systems and methods for predicting the outcome of chaotic systems are described. An example of a prediction system disclosed herein includes, in general, functional elements to vary the initial conditions of a chaotic system and calculate a plurality of possible trajectories for the chaotic system. The prediction system also includes calculating a Lyapunov exponent for each of the plurality of possible trajectories and selecting the trajectory with the smallest Lyapunov exponent as the most likely trajectory to occur.
Claims17
A prediction system for predicting the outcome of a chaotic system, the prediction system comprising:
- means for varying the initial conditions of a chaotic system;
- means for calculating a plurality of possible trajectories for the chaotic system;
- means for calculating a Lyapunov exponent for each of the plurality of possible trajectories;
- and
- means for selecting the trajectory with the smallest Lyapunov exponent as the most likely trajectory to occur.
A method of predicting the likelihood of an outcome in a chaotic system, the method comprising:
- varying initial conditions of a model of a chaotic system;
- calculating multiple trajectories of the chaotic system model based on a number of uncertainty factors;
- calculating a Lyapunov exponent for each of the multiple trajectories;
- and
- comparing the Lyapunov exponents from each of the multiple trajectories to determine the trajectory with the smallest Lyapunov exponent, whereby the trajectory with the smallest Lyapunov exponent is indicative of the likelihood of the outcome of the chaotic system.
A computer program stored on a computer readable medium for execution by a computer, the computer program comprising:
- logic configured to vary the initial conditions of a chaotic system;
- logic configured to calculate a plurality of possible trajectories for the chaotic system;
- logic configured to calculate a Lyapunov exponent for each of the plurality of possible trajectories to determine the trajectory with the smallest Lyapunov exponent;
- and
- logic configured to select the trajectory with the smallest Lyapunov exponent to represent a prediction of an outcome of the chaotic system.
Dependencies are inferred from the claim text.