Nonlinear System

From Ioannis Kourouklides
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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.

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.
  • 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 computation18(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 networks5(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]

See also[edit]

Other Resources[edit]