Articles | Volume 22, issue 6
https://doi.org/10.5194/npg-22-749-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/npg-22-749-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Nonlinear feedback in a six-dimensional Lorenz model: impact of an additional heating term
B.-W. Shen
CORRESPONDING AUTHOR
Department of Mathematics and Statistics, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-7720, USA
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Cited
31 citations as recorded by crossref.
- Multiscale Processes of Hurricane Sandy (2012) as Revealed by the Parallel Ensemble Empirical Mode Decomposition and Advanced Visualization Technology B. Shen et al.
- The 50th Anniversary of the Metaphorical Butterfly Effect since Lorenz (1972): Multistability, Multiscale Predictability, and Sensitivity in Numerical Models B. Shen et al.
- On the dynamics of a high-order Lorenz–Stenflo system P. Rech
- Quasi-Periodic Orbits in the Five-Dimensional Nondissipative Lorenz Model: The Role of the Extended Nonlinear Feedback Loop S. Faghih-Naini & B. Shen
- The Dual Nature of Chaos and Order in the Atmosphere B. Shen et al.
- Periodicity and Chaos of High-Order Lorenz Systems S. Moon et al.
- Hierarchical scale dependence associated with the extension of the nonlinear feedback loop in a seven-dimensional Lorenz model B. Shen
- Ultimate Boundedness and Finite Time Stability for a High Dimensional Fractional-Order Lorenz Model M. Huang et al.
- Study of Rayleigh–Bénard convection in a chemically reactive fluid using a generalized Lorenz model and the cubic–quintic Ginzburg–Landau equation C. Kanchana et al.
- A kernel principal component analysis of coexisting attractors within a generalized Lorenz model J. Cui & B. Shen
- Aggregated Negative Feedback in a Generalized Lorenz Model B. Shen
- Dynamical analysis and boundedness for a generalized chaotic Lorenz model X. Mao et al.
- An Evaluation of the Parallel Ensemble Empirical Mode Decomposition Method in Revealing the Role of Downscaling Processes Associated with African Easterly Waves in Tropical Cyclone Genesis Y. Wu & B. Shen
- Dynamical and chaotic behaviors of natural convection flow in semi-annular cylindrical domains using energy-conserving low-order spectral models A. Khodakaram-Tafti et al.
- Using the (3N)-Dimensional Generalized Lorenz Systems as a Testbed for Data Assimilation: The Ensemble Kalman Filter S. Moon & J. Baik
- High-dimensional generalizations of the Lorenz system and implications for predictability S. Moon et al.
- Dynamics of a High-Order Generalized Lorenz Model for Magnetoconvection N. Pati & P. Rech
- On periodic solutions in the non-dissipative Lorenz model: the role of the nonlinear feedback loop B. Shen
- Chaos synchronization in generalized Lorenz systems and an application to image encryption S. Moon et al.
- Stability and periodicity of high-order Lorenz–Stenflo equations J. Park et al.
- One Saddle Point and Two Types of Sensitivities within the Lorenz 1963 and 1969 Models B. Shen et al.
- Homoclinic Orbits and Solitary Waves within the Nondissipative Lorenz Model and KdV Equation B. Shen
- Frenetic steering: Nonequilibrium-enabled navigation B. Lefebvre & C. Maes
- Time Averages and Periodic Attractors at High Rayleigh Number for Lorenz-like Models I. Ovsyannikov et al.
- Periodicity and chaos of thermal convective flows in annular cylindrical domains using the method of isolation by spectral expansions A. Khodakaram-Tafti et al.
- On the dynamics of five- and six-dimensional Lorenz models C. Felicio & P. Rech
- On the Predictability of 30-Day Global Mesoscale Simulations of African Easterly Waves during Summer 2006: A View with the Generalized Lorenz Model B. Shen
- Period-Bubbling Transition to Chaos in Thermo-Viscoelastic Fluid Systems G. Layek & N. Pati
- A recurrence analysis of chaotic and non-chaotic solutions within a generalized nine-dimensional Lorenz model T. Reyes & B. Shen
- A KdV–SIR Equation and Its Analytical Solutions for Solitary Epidemic Waves W. Paxson & B. Shen
- A Review of Lorenz’s Models from 1960 to 2008 B. Shen
31 citations as recorded by crossref.
- Multiscale Processes of Hurricane Sandy (2012) as Revealed by the Parallel Ensemble Empirical Mode Decomposition and Advanced Visualization Technology B. Shen et al.
- The 50th Anniversary of the Metaphorical Butterfly Effect since Lorenz (1972): Multistability, Multiscale Predictability, and Sensitivity in Numerical Models B. Shen et al.
- On the dynamics of a high-order Lorenz–Stenflo system P. Rech
- Quasi-Periodic Orbits in the Five-Dimensional Nondissipative Lorenz Model: The Role of the Extended Nonlinear Feedback Loop S. Faghih-Naini & B. Shen
- The Dual Nature of Chaos and Order in the Atmosphere B. Shen et al.
- Periodicity and Chaos of High-Order Lorenz Systems S. Moon et al.
- Hierarchical scale dependence associated with the extension of the nonlinear feedback loop in a seven-dimensional Lorenz model B. Shen
- Ultimate Boundedness and Finite Time Stability for a High Dimensional Fractional-Order Lorenz Model M. Huang et al.
- Study of Rayleigh–Bénard convection in a chemically reactive fluid using a generalized Lorenz model and the cubic–quintic Ginzburg–Landau equation C. Kanchana et al.
- A kernel principal component analysis of coexisting attractors within a generalized Lorenz model J. Cui & B. Shen
- Aggregated Negative Feedback in a Generalized Lorenz Model B. Shen
- Dynamical analysis and boundedness for a generalized chaotic Lorenz model X. Mao et al.
- An Evaluation of the Parallel Ensemble Empirical Mode Decomposition Method in Revealing the Role of Downscaling Processes Associated with African Easterly Waves in Tropical Cyclone Genesis Y. Wu & B. Shen
- Dynamical and chaotic behaviors of natural convection flow in semi-annular cylindrical domains using energy-conserving low-order spectral models A. Khodakaram-Tafti et al.
- Using the (3N)-Dimensional Generalized Lorenz Systems as a Testbed for Data Assimilation: The Ensemble Kalman Filter S. Moon & J. Baik
- High-dimensional generalizations of the Lorenz system and implications for predictability S. Moon et al.
- Dynamics of a High-Order Generalized Lorenz Model for Magnetoconvection N. Pati & P. Rech
- On periodic solutions in the non-dissipative Lorenz model: the role of the nonlinear feedback loop B. Shen
- Chaos synchronization in generalized Lorenz systems and an application to image encryption S. Moon et al.
- Stability and periodicity of high-order Lorenz–Stenflo equations J. Park et al.
- One Saddle Point and Two Types of Sensitivities within the Lorenz 1963 and 1969 Models B. Shen et al.
- Homoclinic Orbits and Solitary Waves within the Nondissipative Lorenz Model and KdV Equation B. Shen
- Frenetic steering: Nonequilibrium-enabled navigation B. Lefebvre & C. Maes
- Time Averages and Periodic Attractors at High Rayleigh Number for Lorenz-like Models I. Ovsyannikov et al.
- Periodicity and chaos of thermal convective flows in annular cylindrical domains using the method of isolation by spectral expansions A. Khodakaram-Tafti et al.
- On the dynamics of five- and six-dimensional Lorenz models C. Felicio & P. Rech
- On the Predictability of 30-Day Global Mesoscale Simulations of African Easterly Waves during Summer 2006: A View with the Generalized Lorenz Model B. Shen
- Period-Bubbling Transition to Chaos in Thermo-Viscoelastic Fluid Systems G. Layek & N. Pati
- A recurrence analysis of chaotic and non-chaotic solutions within a generalized nine-dimensional Lorenz model T. Reyes & B. Shen
- A KdV–SIR Equation and Its Analytical Solutions for Solitary Epidemic Waves W. Paxson & B. Shen
- A Review of Lorenz’s Models from 1960 to 2008 B. Shen
Saved (final revised paper)
Discussed (final revised paper)
Latest update: 11 May 2026
Short summary
While the negative nonlinear feedback associated with two new modes in the 5DLM can stabilize solutions, additional resolved heating processes by a third mode in the 6DLM can destabilize solutions. The findings support the view of Lorenz (1972) on the role of small-scale processes: if the flap of a butterfly’s wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado.
While the negative nonlinear feedback associated with two new modes in the 5DLM can stabilize...