Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Volume 20, Issue 8, Pages 2419-2451Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2015.20.2419
Keywords
Lyapunov function; Morse decomposition; combinatorial dynamics; Conley's decomposition theorem; algorithms
Categories
Funding
- NSF [NFS-DMS-0914995, NSF-DMS-0915019, 1125174, 1248071]
- AFOSR
- DARPA
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1125174, 1248071] Funding Source: National Science Foundation
Ask authors/readers for more resources
We present an efficient algorithm for constructing piecewise constant Lyapunov functions for dynamics generated by a continuous nonlinear map defined on a compact metric space. We provide a memory efficient data structure for storing nonuniform grids on which the Lyapunov function is defined and give bounds on the complexity of the algorithm for both time and memory. We prove that if the diameters of the grid elements go to zero, then the sequence of piecewise constant Lyapunov functions generated by our algorithm converge to a continuous Lyapunov function for the dynamics generated the nonlinear map. We conclude by applying these techniques to two problems from population biology.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available