-
Previous Article
HIV infection and CD4+ T cell dynamics
- DCDS-B Home
- This Issue
-
Next Article
Laguerre and composite Legendre-Laguerre Dual-Petrov-Galerkin methods for third-order equations
Revisiting the slow manifold of the Lorenz-Krishnamurthy quintet
| 1. | Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, India |
| 2. | Center for Atmospheric and Oceanic Sciences, Indian Institute of Science, Bangalore 560 012, India |
| 3. | TIFR Centre, Indian Institute of Science, Bangalore 560 012, India |
Minimization of evolution rate does not guarantee the invariance of the manifold. Using a locally linear approximate reduction scheme, the invariance can be maintained. However, the solutions so obtained do develop high frequency oscillations. The onset of these high frequency oscillations is delayed vis-a-vis other previous studies. These methods have potential to be used in improving the predictions of weather systems.
| [1] |
Parker Childs, James P. Keener. Slow manifold reduction of a stochastic chemical reaction: Exploring Keizer's paradox. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1775-1794. doi: 10.3934/dcdsb.2012.17.1775 |
| [2] |
George Osipenko. Linearization near a locally nonunique invariant manifold. Discrete and Continuous Dynamical Systems, 1997, 3 (2) : 189-205. doi: 10.3934/dcds.1997.3.189 |
| [3] |
Ronny Bergmann, Raymond H. Chan, Ralf Hielscher, Johannes Persch, Gabriele Steidl. Restoration of manifold-valued images by half-quadratic minimization. Inverse Problems and Imaging, 2016, 10 (2) : 281-304. doi: 10.3934/ipi.2016001 |
| [4] |
Riccarda Rossi, Ulisse Stefanelli, Marita Thomas. Rate-independent evolution of sets. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 89-119. doi: 10.3934/dcdss.2020304 |
| [5] |
Antonios Zagaris, Christophe Vandekerckhove, C. William Gear, Tasso J. Kaper, Ioannis G. Kevrekidis. Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2759-2803. doi: 10.3934/dcds.2012.32.2759 |
| [6] |
M. Montaz Ali. A recursive topographical differential evolution algorithm for potential energy minimization. Journal of Industrial and Management Optimization, 2010, 6 (1) : 29-46. doi: 10.3934/jimo.2010.6.29 |
| [7] |
J. B. van den Berg, J. D. Mireles James. Parameterization of slow-stable manifolds and their invariant vector bundles: Theory and numerical implementation. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4637-4664. doi: 10.3934/dcds.2016002 |
| [8] |
Marian Gidea, Rafael de la Llave, Tere M. Seara. A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6795-6813. doi: 10.3934/dcds.2020166 |
| [9] |
Jiying Liu, Jubo Zhu, Fengxia Yan, Zenghui Zhang. Compressive sampling and $l_1$ minimization for SAR imaging with low sampling rate. Inverse Problems and Imaging, 2013, 7 (4) : 1295-1305. doi: 10.3934/ipi.2013.7.1295 |
| [10] |
Amina Amassad, Mircea Sofonea. Analysis of some nonlinear evolution systems arising in rate-type viscoplasticity. Conference Publications, 1998, 1998 (Special) : 58-71. doi: 10.3934/proc.1998.1998.58 |
| [11] |
Ulisse Stefanelli, Daniel Wachsmuth, Gerd Wachsmuth. Optimal control of a rate-independent evolution equation via viscous regularization. Discrete and Continuous Dynamical Systems - S, 2017, 10 (6) : 1467-1485. doi: 10.3934/dcdss.2017076 |
| [12] |
Ziang Long, Penghang Yin, Jack Xin. Global convergence and geometric characterization of slow to fast weight evolution in neural network training for classifying linearly non-separable data. Inverse Problems and Imaging, 2021, 15 (1) : 41-62. doi: 10.3934/ipi.2020077 |
| [13] |
Pei Wang, Ling Zhang, Zhongfei Li. Asset allocation for a DC pension plan with learning about stock return predictability. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021138 |
| [14] |
E. Camouzis, H. Kollias, I. Leventides. Stable manifold market sequences. Journal of Dynamics and Games, 2018, 5 (2) : 165-185. doi: 10.3934/jdg.2018010 |
| [15] |
Camillo De Lellis, Emanuele Spadaro. Center manifold: A case study. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1249-1272. doi: 10.3934/dcds.2011.31.1249 |
| [16] |
Zhiguo Feng, Ka-Fai Cedric Yiu. Manifold relaxations for integer programming. Journal of Industrial and Management Optimization, 2014, 10 (2) : 557-566. doi: 10.3934/jimo.2014.10.557 |
| [17] |
Weinan E, Weiguo Gao. Orbital minimization with localization. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 249-264. doi: 10.3934/dcds.2009.23.249 |
| [18] |
Meijuan Shang, Yanan Liu, Lingchen Kong, Xianchao Xiu, Ying Yang. Nonconvex mixed matrix minimization. Mathematical Foundations of Computing, 2019, 2 (2) : 107-126. doi: 10.3934/mfc.2019009 |
| [19] |
Justin Holmer, Maciej Zworski. Slow soliton interaction with delta impurities. Journal of Modern Dynamics, 2007, 1 (4) : 689-718. doi: 10.3934/jmd.2007.1.689 |
| [20] |
Debora Amadori, Wen Shen. Front tracking approximations for slow erosion. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1481-1502. doi: 10.3934/dcds.2012.32.1481 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]