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
 * Bifurcation Theory
 * Limit Cycles
 * Hamiltonian Dynamics
 * Lagrangian dynamics
 * Langevin 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.
 * 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 NIPS (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

Other Resources

 * Dynamical Systems - Scholarpedia
 * Complex Systems - Scholarpedia
 * Volterra and Wiener Series - Scholarpedia
 * Hamiltonian Systems - Scholarpedia
 * Dynamical Systems and Chaos - Notebook