Method for characterizing dynamical systems
First Claim
1. A method for characterizing a degree of similarity between phase space representations of trajectories arising from different dynamical systems comprising the steps of:
- designating a first one of said trajectories as a template against which others of said trajectories are to be compared;
determining a measure of a shortest distance in phase space of each point of a second trajectory to said template trajectory; and
determining the largest of said shortest distances to provide a characterizing value.
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Abstract
A method for characterizing the degree of similarity between phase space representations of trajectories of different dynamical systems. This method provides a computationally efficient technique for comparing different dynamical systems, or different dynamics exhibited by the same system. A first trajectory is designated as a template against which other trajectories are compared. A test trajectory is characterized by providing a measure based on determining the smallest distance between each point of the test trajectory to the template and then determining the largest of these smallest distances. The similarity of the two trajectories is quantified by establishing a lattice or grid for the phase space. For each lattice point, the distance, as given by a metric defined for the space, is calculated to the nearest point of the template trajectory. The minimum distance is retained and associated in a memory for each lattice point. The test trajectory is generated in the phase space with each data point of the test trajectory landing in a bin having a lattice point at its center. The previously determined shortest distance of that lattice point to the template trajectory is fetched from memory to provide an approximation of the closest distance of each point in the test trajectory to the template trajectory. The maximum of these distances among all points in the test trajectory serves as the distance between the two trajectories, and hence as a measure of degree of similarity between the two trajectories.
92 Citations
18 Claims
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1. A method for characterizing a degree of similarity between phase space representations of trajectories arising from different dynamical systems comprising the steps of:
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designating a first one of said trajectories as a template against which others of said trajectories are to be compared; determining a measure of a shortest distance in phase space of each point of a second trajectory to said template trajectory; and determining the largest of said shortest distances to provide a characterizing value. - View Dependent Claims (2, 3, 4, 5)
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6. A method for characterizing a degree of similarity between phase space representations of trajectories of different dynamical systems comprising the steps of:
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designating a first trajectory as a template against which other trajectories are compared; establishing a lattice for the phase space; determining a measure of a distance from each lattice point to a closest point of said template trajectories and storing said measure in a memory; determining a closest lattice point for each data point of a second trajectory and fetching said distance measure from said lattice point from said memory; and determining a largest of said measures fetched from said memory to characterize said test trajectory. - View Dependent Claims (7, 8)
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9. A system for characterizing a degree of similarity between phase space representations of trajectories arising from different dynamical systems comprising:
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means for designating a first one of said trajectories as a template against which others of said trajectories are to be compared; means for determining a measure of a shortest distance in phase space of each point of a second trajectory to said template trajectory; and means for determining the largest of said shortest distances to provide a characterizing value.
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10. A method for characterizing a degree of similarity between phase space representations of trajectories arising from different dynamics of a dynamical system comprising the steps of:
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designating a first one of said trajectories as a template against which others of said trajectories are to be compared; determining a measure of a shortest distance in phase space of each point of a second trajectory to said template trajectory; and determining the largest of said shortest distances to provide a characterizing value. - View Dependent Claims (11, 12, 13, 14)
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15. A method for characterizing a degree of similarity between phase space representations of trajectories of different dynamics of a dynamical system comprising the steps of:
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designating a first trajectory as a template against which other trajectories are compared; establishing a lattice for the phase space; determining a measure of a distance from each lattice point to a closest point of said template trajectory and storing said measure in a memory; determining a closest lattice point for each data point of a second trajectory and fetching said distance measure from said lattice point from said memory; and determining a largest of said measures fetched from said memory to characterize said test trajectory. - View Dependent Claims (16, 17)
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18. A system for characterizing a degree of similarity between phase space representations of different trajectories of a given dynamical system comprising:
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means for designating a first one of said trajectories as a template against which others of said trajectories are to be compared; means for determining a measure of a shortest distance in phase space of each point of a second trajectory to said template trajectory; and means for determining the largest of said shortest distances to provide a characterizing value.
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Specification