Nonlinear System

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

• 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)

Books and Book Chapters

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

• 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

• Control System Toolbox - MATLAB
• System Identification Toolbox - MATLAB
• Python Control Systems Toolbox
• dynpy - Python
• PyDSTool - Python
• DLM - R
• simecol - R

See also

• Control Theory
• Estimation Theory / Statistical Signal Processing
• Linear Dynamical Systems
• Kernel Methods
• Monte Carlo Methods

Other Resources

• Dynamical Systems - Scholarpedia
• Volterra and Wiener Series - Scholarpedia
• Hamiltonian Systems - Scholarpedia
• Dynamical Systems and Chaos - Notebook
• Molecular and Stochastic Dynamics - Notes