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

• chaosbook.org: Cvitanović, free and updated
• Sprott's strange-attractor gallery
• Scholarpedia: Dynamical systems articles
• DynamicalSystems.jl documentation
• Complexity Explorer (SFI MOOC)

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)