Dynamical systems and chaos

Research papers

Robert L. Axtell & J. Doyne Farmer, (2025). 'Agent-Based Modeling in Economics and Finance: Past, Present, and Future'. Journal of Economic Literature 63 (1): 197–287.2025. DOI: 10.1257/jel.20221319

Robert L. Axtell & J. Doyne Farmer, (2022). 'Agent-Based Modeling in Economics and Finance: Past, Present, and Future'. INET Oxford Working Paper No. 2022-10.
Jaume Masoliver, Miquel Montero, Josep Perelló, J. Doyne Farmer, John Geanakoplos. “Valuing the Future and Discounting in Random Environments: A Review.” Entropy 2022, 24, 496.
Marco Pangallo, James Sanders, Tobias Galla and J. Doyne Farmer, “A Taxonomy of Learning Dynamics in 2 × 2 Games”. Games and Economic Behavior, Vol 132 (2022)

Blas Kolic, Juan Sabuco, and J. Doyne Farmer (2021). “Estimating initial conditions for dynamical systems with incomplete information”. INET Oxford Working Paper No. 2021-20.

Marco Pangallo, Torsten Heinrich and J. Doyne Farmer, “Best reply structure and equilibrium convergence in generic games”, Science Advances 5(2). DOI: 10.1126/sciadv.aat1328 (2019).

James B. T. Sanders, J. Doyne Farmer and Tobias Galla, “The Prevalence of Chaotic Dynamics in Games with Many Players”, Nature (2018)

Marco Pangallo, James Sanders, J. Doyne Farmer and Tobias Galla, “A Taxonomy of Learning Dynamics in 2 × 2 Games”, https://papers.ssrn.com (2017).

Christoph Aymanns and J. Doyne Farmer, “Dynamics of the Leverage Cycle”, Journal of Economic Dynamics and Control 50, 155-179 (2015)

Y. Zou, J. Heitzig, R.V. Donner, J.F. Donges, J.D. Farmer, R. Meucci, S. Euzzor, N. Marwan, J. Kurths, "Power-laws in recurrence networks from dynamical systems", Europhysics Letters 98 (4) 48001 (2012).1982

James Theiler, Bryan Galdrikian, Andrew Longtin, Stephen Eubank and J. Doyne Farmer, “Detecting Nonlinear Structure in Time Series”, Physica D 58 (1992): 77-94.
John F. Gibson, J. Doyne Farmer, Martin Casdagli and Stephen Eubank, “An Analytic Approach to Practical State Space Reconstruction”, Physica D 57(1-2) (1992): 1-30.
Ute Dressler, and J. Doyne Farmer, “Lyapunov Exponents for Higher Order Derivatives”, Physica D 59 (1992): 365-377.
Robert J. Deissler and J. Doyne Farmer, “Deterministic Noise Amplifiers”, Physica D 55(1-2) (1992): 155-165.
Ute Dressler, and J. Doyne Farmer, “Generalized Lyapunov exponents corresponding to higher derivatives”, Physica D 59 (1992): 365-377.

Martin Casdagli, Stephen Eubank, J. Doyne Farmer and John Gibson, “State Space Reconstruction in the Presence of Noise”, Physica D 51(1-3) (1991): 52-98.
J. Doyne Farmer and John J. Sidorowich, “Optimal Shadowing and Noise Reduction”, Physica D 47(3) (1991): 373-392.

Robert Ecke, J. Doyne Farmer and David K. Umberger, “Scaling of the Arnold Tongues”, Nonlinearity 2(2) (1989): 175-196.

J. Doyne Farmer and John J. Sidorowich, “Predicting Chaotic Time Series”, Physical Review Letters 59(8) (1987): 845-848.

James D. Keeler and J. Doyne Farmer, “Robust Space-Time Intermittency and 1/f Noise”, Physica D 23(1-3) (1986): 413-435.
James P. Crutchfield, J. Doyne Farmer, Norman H. Packard and Robert S. Shaw. “Chaos.” Scientific American 255(6) (1986): 46-57.
R. J. Bagley, J. D. Farmer and G. Mayer-Kress, “Mode Locking, the Belousov-Zhabotinsky Reaction, and One-Dimensional Mappings”, Physics Letters A 114(8) (1986): 419-423.
J. Doyne Farmer, Indubala I. Satija and David K. Umberger, “A Universal Strange Attractor Underlying the Quasiperiodic Transition to Chaos”, Physics Letters A 114(7) (1986): 341-345.

David K. Umberger and J. Doyne Farmer, “Fat Fractals on the Energy Surface”, Physical Review Letters 55(7) (1985): 661-664.
J. Doyne Farmer, “Sensitive Dependence on Parameters in Nonlinear Dynamics”, Physical Review Letters 55(4) (1985): 351-355.
J. Doyne Farmer and Indubala I. Satija, “Renormalization of the Quasiperiodic Transition to Chaos for Arbitrary Winding Numbers”, Physical Review A 31(5) (1985): 3520-3522.
David Campbell, Jim Crutchfield, J. Doyne Farmer and Erica Jen, “Experimental Mathematics: The Role of Computation in Nonlinear Studies”, Comm. ACM 28(4) (1985): 374-384.

A. Brandstater, J. Swift, Harry L. Swinney, A. Wolf, J. Doyne Farmer, Erica Jen and Jim Crutchfield. “Low-Dimensional Chaos in a Hydrodynamic System”, Physical Review Letters 51(16) (1983): 1442-1445.
J D. Farmer, Edward Ott and James A. Yorke, “The Dimension of Chaotic Attractors”, Physica D 7(1-3) (1983): 153-180.

James P. Crutchfield, J. Doyne Farmer and B. J. Huberman, “Fluctuations and Chaotic Dynamics”, Physics Reports 92(2) (1982): 47-82.
J. Doyne Farmer, “Information Dimension and the Probabilistic Structure of Chaos”, Z. Naturforsch 37(11) (1982): 1304-1325.
J. Doyne Farmer, John Hart and Patrick Weidman, “A Phase Space Analysis of Baroclinic Flow”, Physics Letters A 91(1) (1982): 22-24.
J. Doyne Farmer, “Chaotic Attractors of an Infinite-Dimensional Dynamical System”, Physica D 4(3) (1982): 366-393.

Harold, Froehling, James P. Crutchfield, J. Doyne Farmer, Norman H. Packard and Rob Shaw, “On Determining the Dimension of Chaotic Flows”, Physica D 3(3) (1981): 605-617.

J. Doyne Farmer, “Spectral Broadening of Period-Doubling Bifurcation Sequences”, Physical Review Letters 47(3) (1980): 179-182.
J. Doyne Farmer, James P. Crutchfield, Harold Froehling, Norman Packard and Rob Shaw, “Power Spectra and Mixing Properties of Strange Attractors”, Annals of the New York Academy of Sciences 375 (1980): 453-472.
Norman H. Packard, James P. Crutchfield, J. Doyne Farmer and Robert S. Shaw, “Geometry from a Time Series”, Physical Review Letters 45(9) (1980): 712-716.
James D. Crutchfield, J. Doyne Farmer, Norman Packard, R. Shaw, G. Jones and R. Donnelly, “Power Spectral Analysis of a Dynamical System”, Physics Letters A 76(1) (1980): 1-4.