Reference

References

Foundational papers

Lorenz, E. N. (1963). “Deterministic nonperiodic flow”. J. Atmos. Sci..
Smale, S. (1967). “Differentiable dynamical systems”. Bull. AMS.
Li, T.-Y. & Yorke, J. (1975). “Period three implies chaos”. Amer. Math. Monthly.
Ruelle, D. & Takens, F. (1971). “On the nature of turbulence”. Comm. Math. Phys..
May, R. (1976). “Simple mathematical models with very complicated dynamics”. Nature.
Rössler, O. (1976). “An equation for continuous chaos”. Phys. Lett. A.
Hénon, M. (1976). “A two-dimensional mapping with a strange attractor”. Comm. Math. Phys..
Feigenbaum, M. (1978). “Quantitative universality for a class of nonlinear transformations”. J. Stat. Phys..
Pomeau, Y. & Manneville, P. (1980). “Intermittent transition to turbulence in dissipative dynamical systems”. Comm. Math. Phys..
Takens, F. (1981). “Detecting strange attractors in turbulence”. Lecture Notes in Math..
Grassberger, P. & Procaccia, I. (1983). “Characterization of strange attractors”. Phys. Rev. Lett..
Wolf, A., Swift, J., Swinney, H., Vastano, J. (1985). “Determining Lyapunov exponents from a time series”. Physica D.
Pecora, L. & Carroll, T. (1990). “Synchronization in chaotic systems”. Phys. Rev. Lett..
Ott, E., Grebogi, C., Yorke, J. (1990). “Controlling chaos”. Phys. Rev. Lett..
Pyragas, K. (1992). “Continuous control of chaos by self-controlling feedback”. Phys. Lett. A.
Kennel, M., Brown, R., Abarbanel, H. (1992). “Determining embedding dimension via false nearest neighbours”. Phys. Rev. A.
Rosenstein, M., Collins, J., De Luca, C. (1993). “A practical method for calculating largest Lyapunov exponents”. Physica D.
Kantz, H. (1994). “A robust method to estimate the maximal Lyapunov exponent”. Phys. Lett. A.
Sprott, J. C. (1994). “Some simple chaotic flows”. Phys. Rev. E.
Bandt, C. & Pompe, B. (2002). “Permutation entropy: a natural complexity measure”. Phys. Rev. Lett..
Gottwald, G. & Melbourne, I. (2004). “A new test for chaos in deterministic systems”. Proc. R. Soc. A.
Alvarez, G. & Li, S. (2006). “Some basic cryptographic requirements for chaos-based cryptosystems”. Int. J. Bifurc. Chaos.
Marwan, N. et al. (2007). “Recurrence plots for the analysis of complex systems”. Phys. Rep..

Textbooks

Strogatz, Nonlinear Dynamics and Chaos (2nd ed., 2014)
Ott, Chaos in Dynamical Systems (2nd ed., 2002)
Devaney, An Introduction to Chaotic Dynamical Systems (3rd ed., 2021)
Alligood, Sauer & Yorke, Chaos: An Introduction to Dynamical Systems (1996)
Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (2nd ed., 2003)
Guckenheimer & Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (1983)
Hilborn, Chaos and Nonlinear Dynamics (2nd ed., 2000)
Kantz & Schreiber, Nonlinear Time Series Analysis (2nd ed., 2003)
Sprott, Chaos and Time-Series Analysis (2003)
Tabor, Chaos and Integrability in Nonlinear Dynamics (1989)
Schuster & Just, Deterministic Chaos (4th ed., 2005)
Tél & Gruiz, Chaotic Dynamics: An Introduction Based on Classical Mechanics (2006)
Lichtenberg & Lieberman, Regular and Chaotic Dynamics (2nd ed., 1992)
Cvitanović et al., Chaos Book, chaosbook.org (open source, regularly updated)
Hirsch, Smale, Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos (3rd ed., 2012)
Mandelbrot, The Fractal Geometry of Nature (1982)
Peitgen, Jürgens, Saupe, Chaos and Fractals (2nd ed., 2004)
Gleick, Chaos: Making a New Science (1987), popular
Stewart, Does God Play Dice? (2nd ed., 2002), popular

Journals

Chaos (AIP)
Physica D: Nonlinear Phenomena
International Journal of Bifurcation and Chaos
Chaos, Solitons & Fractals
Communications in Nonlinear Science and Numerical Simulation
Nonlinear Dynamics (Springer)
Phys. Rev. E
SIAM Journal on Applied Dynamical Systems
Nonlinearity (IOP)
Journal of Nonlinear Science
Regular and Chaotic Dynamics

Online resources

Software ecosystems

Julia: DynamicalSystems.jl, ChaosTools.jl, Attractors.jl, DifferentialEquations.jl, DelayDiffEq.jl
Python: scipy.integrate, nolds, pyrqa, pyEDM, dysts
C/Fortran: TISEAN (Hegger & Kantz), classic toolkit for nonlinear time-series analysis
MATLAB: Chaos Data Analyzer (Sprott)