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Polynomial optimization with applications to stability analysis and control - Alternatives to sum of squares
Efficient computation of Lyapunov functions for Morse decompositions
1. | Rutgers University, 110 Frelinghusen Road, Piscataway, NJ 08854, United States, United States |
2. | Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, 33431 Boca Raton |
3. | Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, United States |
References:
[1] |
Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka and P. Pilarczyk, A database schema for the analysis of global dynamics of multiparameter systems,, SIAM Journal on Applied Dynamical Systems, 8 (2009), 757.
doi: 10.1137/080734935. |
[2] |
L. Arge, The buffer tree: A technique for designing batched external data structures,, Algorithmica, 37 (2003), 1.
doi: 10.1007/s00453-003-1021-x. |
[3] |
H. Ban and W. D. Kalies, A computational approach to Conley's decomposition theorem,, Journal of Computational Nonlinear Dynamics, 1 (2006), 312.
doi: 10.1115/1.2338651. |
[4] |
J. Bush, M. Gameiro, S. Harker, H. Kokubu, K. Mischaikow, I. Obayashi and P. Pilarczyk, Combinatorial-topological framework for the analysis of global dynamics,, Chaos: An Interdisciplinary Journal of Nonlinear Science, 22 (2012).
doi: 10.1063/1.4767672. |
[5] |
F. Claude and G. Navarro, Practical rank/select queries over arbitrary sequences,, in String Processing and Information Retrieval, (5280), 176.
doi: 10.1007/978-3-540-89097-3_18. |
[6] |
C. Conley, Isolated Invariant Sets and the Morse Index,, CBMS Regional Conference Series in Mathematics, (1978).
|
[7] |
J. M. Cushing, S. Levarge, N. Chitnis and S. M. Henson, Some discrete competition models and the competitive exclusion principle,, Journal of difference Equations and Applications, 10 (2004), 1139.
doi: 10.1080/10236190410001652739. |
[8] |
E. W. Dijkstra, A note on two problems in connexion with graphs,, Numerische mathematik, 1 (1959), 269.
doi: 10.1007/BF01386390. |
[9] |
M. L. Fredman and R. E. Tarjan, Fibonacci heaps and their uses in improved network optimization algorithms,, Journal of the ACM (JACM), 34 (1987), 596.
doi: 10.1145/28869.28874. |
[10] |
S. Gog, T. Beller, A. Moffat and M. Petri, From theory to practice: Plug and play with succinct data structures,, in Experimental Algorithms, (8504), 326.
doi: 10.1007/978-3-319-07959-2_28. |
[11] |
A. Goullet, S. Harker, D. Kasti, W. Kalies and K. Mischaikow, Supplementary materials,, , (2014). Google Scholar |
[12] |
S. Harker, Space efficient variants of Tarjan's algorithm for strongly connected components,, 2014., (). Google Scholar |
[13] |
S, Harker and A, Goullet, et al., Conley-Morse-Database software package,, 2014., (). Google Scholar |
[14] |
G. Jacobson, Space-efficient static trees and graphs,, in Foundations of Computer Science, (1989), 549.
doi: 10.1109/SFCS.1989.63533. |
[15] |
J. Jansson, K. Sadakane and W.-K. Sung, Ultra-succinct representation of ordered trees with applications,, Journal of Computer and System Sciences, 78 (2012), 619.
doi: 10.1016/j.jcss.2011.09.002. |
[16] |
B. Jiang, I/O-and CPU-optimal recognition of strongly connected components,, Information Processing Letters, 45 (1993), 111.
doi: 10.1016/0020-0190(93)90011-W. |
[17] |
W. D. Kalies, K. Mischaikow, and R. C. A. M. VanderVorst, An algorithmic approach to chain recurrence,, Found. Comput. Math., 5 (2005), 409.
doi: 10.1007/s10208-004-0163-9. |
[18] |
W. D. Kalies, K. Mischaikow and R. C. A. M. VanderVorst, Lattice structures for attractors I,, Journal of Computational Dynamics, (2014). Google Scholar |
[19] |
W. D. Kalies, K. Mischaikow and R. C. A. M. VanderVorst, Lattice structures for attractors II,, in preparation, (2014). Google Scholar |
[20] |
W. D. Kalies, K. Mischaikow and R. C. A. M. VanderVorst, Lattice structures for attractors III,, in preparation, (2014). Google Scholar |
[21] |
R. P. McGehee and T. Wiandt, Conley decomposition for closed relations,, J. Difference Equ. Appl., 12 (2006), 1.
doi: 10.1080/00207210500171620. |
[22] |
R. McGehee, Attractors for closed relations on compact Hausdorff spaces,, Indiana Univ. Math. J., 41 (1992), 1165.
doi: 10.1512/iumj.1992.41.41058. |
[23] |
J. I. Munro and V. Raman, Succinct representation of balanced parentheses and static trees,, SIAM Journal on Computing, 31 (2001), 762.
doi: 10.1137/S0097539799364092. |
[24] |
R. C. Robinson, An Introduction to Dynamical Systems-Continuous and Discrete,, Second edition, (2012).
|
[25] |
A. Szymczak, A combinatorial procedure for finding isolating neighbourhoods and index pairs,, Proc. Roy. Soc. Edinburgh Sect. A, 127 (1997), 1075.
doi: 10.1017/S0308210500026901. |
[26] |
R. Tarjan, Depth-first search and linear graph algorithms,, SIAM Journal on Computing, 1 (1972), 146.
doi: 10.1137/0201010. |
[27] |
I. Ugarcovici and H. Weiss, Chaotic dynamics of a nonlinear density dependent population model,, Nonlinearity, 17 (2004), 1689.
doi: 10.1088/0951-7715/17/5/007. |
[28] |
J. S. Vitter, Algorithms and data structures for external memory,, Foundations and Trends® in Theoretical Computer Science, 2 (2008), 305.
doi: 10.1561/0400000014. |
[29] |
T. Wiandt, Liapunov functions for closed relations,, J. Difference Equ. Appl., 14 (2008), 705.
doi: 10.1080/10236190701809315. |
show all references
References:
[1] |
Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka and P. Pilarczyk, A database schema for the analysis of global dynamics of multiparameter systems,, SIAM Journal on Applied Dynamical Systems, 8 (2009), 757.
doi: 10.1137/080734935. |
[2] |
L. Arge, The buffer tree: A technique for designing batched external data structures,, Algorithmica, 37 (2003), 1.
doi: 10.1007/s00453-003-1021-x. |
[3] |
H. Ban and W. D. Kalies, A computational approach to Conley's decomposition theorem,, Journal of Computational Nonlinear Dynamics, 1 (2006), 312.
doi: 10.1115/1.2338651. |
[4] |
J. Bush, M. Gameiro, S. Harker, H. Kokubu, K. Mischaikow, I. Obayashi and P. Pilarczyk, Combinatorial-topological framework for the analysis of global dynamics,, Chaos: An Interdisciplinary Journal of Nonlinear Science, 22 (2012).
doi: 10.1063/1.4767672. |
[5] |
F. Claude and G. Navarro, Practical rank/select queries over arbitrary sequences,, in String Processing and Information Retrieval, (5280), 176.
doi: 10.1007/978-3-540-89097-3_18. |
[6] |
C. Conley, Isolated Invariant Sets and the Morse Index,, CBMS Regional Conference Series in Mathematics, (1978).
|
[7] |
J. M. Cushing, S. Levarge, N. Chitnis and S. M. Henson, Some discrete competition models and the competitive exclusion principle,, Journal of difference Equations and Applications, 10 (2004), 1139.
doi: 10.1080/10236190410001652739. |
[8] |
E. W. Dijkstra, A note on two problems in connexion with graphs,, Numerische mathematik, 1 (1959), 269.
doi: 10.1007/BF01386390. |
[9] |
M. L. Fredman and R. E. Tarjan, Fibonacci heaps and their uses in improved network optimization algorithms,, Journal of the ACM (JACM), 34 (1987), 596.
doi: 10.1145/28869.28874. |
[10] |
S. Gog, T. Beller, A. Moffat and M. Petri, From theory to practice: Plug and play with succinct data structures,, in Experimental Algorithms, (8504), 326.
doi: 10.1007/978-3-319-07959-2_28. |
[11] |
A. Goullet, S. Harker, D. Kasti, W. Kalies and K. Mischaikow, Supplementary materials,, , (2014). Google Scholar |
[12] |
S. Harker, Space efficient variants of Tarjan's algorithm for strongly connected components,, 2014., (). Google Scholar |
[13] |
S, Harker and A, Goullet, et al., Conley-Morse-Database software package,, 2014., (). Google Scholar |
[14] |
G. Jacobson, Space-efficient static trees and graphs,, in Foundations of Computer Science, (1989), 549.
doi: 10.1109/SFCS.1989.63533. |
[15] |
J. Jansson, K. Sadakane and W.-K. Sung, Ultra-succinct representation of ordered trees with applications,, Journal of Computer and System Sciences, 78 (2012), 619.
doi: 10.1016/j.jcss.2011.09.002. |
[16] |
B. Jiang, I/O-and CPU-optimal recognition of strongly connected components,, Information Processing Letters, 45 (1993), 111.
doi: 10.1016/0020-0190(93)90011-W. |
[17] |
W. D. Kalies, K. Mischaikow, and R. C. A. M. VanderVorst, An algorithmic approach to chain recurrence,, Found. Comput. Math., 5 (2005), 409.
doi: 10.1007/s10208-004-0163-9. |
[18] |
W. D. Kalies, K. Mischaikow and R. C. A. M. VanderVorst, Lattice structures for attractors I,, Journal of Computational Dynamics, (2014). Google Scholar |
[19] |
W. D. Kalies, K. Mischaikow and R. C. A. M. VanderVorst, Lattice structures for attractors II,, in preparation, (2014). Google Scholar |
[20] |
W. D. Kalies, K. Mischaikow and R. C. A. M. VanderVorst, Lattice structures for attractors III,, in preparation, (2014). Google Scholar |
[21] |
R. P. McGehee and T. Wiandt, Conley decomposition for closed relations,, J. Difference Equ. Appl., 12 (2006), 1.
doi: 10.1080/00207210500171620. |
[22] |
R. McGehee, Attractors for closed relations on compact Hausdorff spaces,, Indiana Univ. Math. J., 41 (1992), 1165.
doi: 10.1512/iumj.1992.41.41058. |
[23] |
J. I. Munro and V. Raman, Succinct representation of balanced parentheses and static trees,, SIAM Journal on Computing, 31 (2001), 762.
doi: 10.1137/S0097539799364092. |
[24] |
R. C. Robinson, An Introduction to Dynamical Systems-Continuous and Discrete,, Second edition, (2012).
|
[25] |
A. Szymczak, A combinatorial procedure for finding isolating neighbourhoods and index pairs,, Proc. Roy. Soc. Edinburgh Sect. A, 127 (1997), 1075.
doi: 10.1017/S0308210500026901. |
[26] |
R. Tarjan, Depth-first search and linear graph algorithms,, SIAM Journal on Computing, 1 (1972), 146.
doi: 10.1137/0201010. |
[27] |
I. Ugarcovici and H. Weiss, Chaotic dynamics of a nonlinear density dependent population model,, Nonlinearity, 17 (2004), 1689.
doi: 10.1088/0951-7715/17/5/007. |
[28] |
J. S. Vitter, Algorithms and data structures for external memory,, Foundations and Trends® in Theoretical Computer Science, 2 (2008), 305.
doi: 10.1561/0400000014. |
[29] |
T. Wiandt, Liapunov functions for closed relations,, J. Difference Equ. Appl., 14 (2008), 705.
doi: 10.1080/10236190701809315. |
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