Nonlinear System

This page contains resources about Nonlinear Systems, Nonlinear Systems Theory, Nonlinear Dynamics, Nonlinear Dynamical Systems and Nonlinear Control, including Nonlinear Time Series.

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.
• 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