Nonlinear System
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This page contains resources about Nonlinear Systems, Nonlinear Systems Theory, Nonlinear Dynamics, Nonlinear Dynamical Systems and Nonlinear Control, including Nonlinear Time Series and Nonlinear System Identification
Subfields and Concepts[edit]
- Chaos Theory / Chaotic Maps
- Coupled Map Lattice
- Bifurcation Theory
- Limit Cycles
- Lotka–Volterra Model / Predator–Prey Model
- Mackey-Glass Model
- Hamiltonian Dynamics
- Lagrangian Dynamics
- Langevin Dynamics
- Brownian Dynamics
- Relativistic Dynamics
- Stochastic Dynamics
- Nonlinear Systems
- Volterra Series Model
- Wiener Series Model
- Nonlinear Autoregressive Moving Average (NARMA) Model
- NARMA exogenous (NARMAX) Model
- Recurrent Neural Network (RNN)
Online Courses[edit]
Video Lectures[edit]
Lecture Notes[edit]
Books and Book Chapters[edit]
See Further Reading and References for more books.
- Strogatz, S. H. (2014). Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Westview press.
- Billings, S. A. (2013). Nonlinear system identification: NARMAX methods in the time, frequency, and spatio-temporal domains. John Wiley & Sons.
- Schlick, T. (2010). "Chapter 13: Molecular Dynamics - Further Topics". Molecular Modeling and Simulation: An Interdisciplinary Guide. Springer Science & Business Media.
- Willi-Hans, S. (2005). The Nonlinear Workbook. World Scientific.
- Kantz, H., & Schreiber, T. (2004). Nonlinear Time Series Analysis. Cambridge University Press.
- Wiggins, S. (2003). Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer-Verlag.
- Khalil, H. K., & Grizzle, J. W. (2002). Nonlinear systems. 3rd Ed. Prentice Hall.
- Thompson, J. M. T., & Stewart, H. B. (2002). Nonlinear dynamics and chaos. John Wiley & Sons.
- Vidyasagar, M. (2002). Nonlinear systems analysis. Prentice Hall.
- Sprott, J. C. (2001). Chaos and time-series analysis. Oxford University Press.
- Mathews, V.J. and Sicuranza , G.L. (2000). Polynomial signal processing. Wiley.
- Sastry, S. S. (1999). Nonlinear systems: analysis, stability, and control. Springer Science & Business Media.
- Henson, M. A., & Seborg, D. E. (1997). Nonlinear process control. Prentice Hall PTR.
- Isidori, A. (1995). Nonlinear control systems. Springer Science & Business Media.
- Rugh, W. J. (1981). Nonlinear system theory. Johns Hopkins University Press.
- Schetzen, M. (1980). The Volterra and Wiener theories of nonlinear systems. Wiley.
- Luenberger, D. G. (1979). Introduction to dynamic systems. John Wiley & Sons.
Scholarly Articles[edit]
- Franz, M. O., & Schölkopf, B. (2006). A unifying view of Wiener and Volterra theory and polynomial kernel regression. Neural computation, 18(12), 3097-3118.
- Connor, J. T., Martin, R. D., & Atlas, L. E. (1994). Recurrent neural networks and robust time series prediction. IEEE transactions on neural networks, 5(2), 240-254.
- Connor, J., Atlas, L. E., & Martin, D. R. (1991). Recurrent networks and NARMA modeling. In Advances in Neural Information Processing Systems (pp. 301-308).
- Brilliant, M. B. (1958). Theory of the analysis of nonlinear systems. RLE Technical Report, No. 345. MIT.
Software[edit]
- Control System Toolbox - MATLAB
- System Identification Toolbox - MATLAB
- Python Control Systems Toolbox
- dynpy - Python
- PyDSTool - Python
- DLM - R
- simecol - R
See also[edit]
- Control Theory
- Estimation Theory / Statistical Signal Processing
- Linear Dynamical Systems
- Kernel Methods
- Monte Carlo Methods
Other Resources[edit]
- Dynamical Systems - Scholarpedia
- Volterra and Wiener Series - Scholarpedia
- Hamiltonian Systems - Scholarpedia
- Dynamical Systems and Chaos - Notebook
- Molecular and Stochastic Dynamics - Notes