BioCircuits Institute

(formerly: Institute for Nonlinear Science)

University of California, San Diego

email: pbryant@ucsd.edu

- Selected scientific papers
- PhD Thesis
- Scientific software (Parameter estimation, Lyapunov exponents)

- Paul H. Bryant, On the interactive beating-modes model: generation of asymmetric multiplet structures and explanation of the Blazhko effect, ApJ
**818**, 53 (2016). - Paul H. Bryant, Is the Blazhko effect the beating of a near resonant double-mode pulsation?, ApJ
**802**, 52 (2015). - Paul H. Bryant, A hybrid mode model of the Blazhko Effect, shown to accurately fit Kepler data for RR Lyr, ApJ
**783**, L15 (2014). - Paul H. Bryant, Optimized synchronization of chaotic and hyperchaotic systems, Phys. Rev. E
**82**, 015201(R) (2010). - Paul H. Bryant and J. M. Nichols, Modeling and detecting localized nonlinearity in continuum systems with a multistage transform, Phys. Rev. E
**81**, 026209 (2009). - John C. Quinn, Paul H. Bryant, Daniel R. Creveling, Sallee R. Klein and Henry D. I. Abarbanel, Parameter and state estimation of experimental chaotic systems using synchronization, Phys. Rev. E
**80**, 016201 (2009). - Paul Bryant, Reggie Brown and Henry D. I. Abarbanel, Lyapunov Exponents from Observed Time Series, Phys. Rev. Lett.
**65**, 1523 (1990). - Paul Bryant, Extensional singularity dimensions for strange attractors, Phys. Lett. A
**179**, 186 (1993). - P. H. Bryant, R. Movshovich and B. Yurke, Noise rise in nondegenerate parametric amplifiers, Phys. Rev. Lett
**66**, 2641 (1991). - Paul Bryant, Kurt Wiesenfeld and Bruce McNamara, Noise rise in parametric amplifiers, Phys. Rev. B
**36**, 752 (1987). - Paul Bryant and Kurt Wiesenfeld, Suppression of period-doubling and nonlinear parametric effects in periodically perturbed systems, Phys. Rev. A
**33**, 2525 (1986). - Reggie Brown, Paul Bryant and Henry D. I. Abarbanel, Computing the Lyapunov spectrum of a dynamical system from an observed time series, Phys. Rev. A
**43**, 2787 (1991). - Paul Bryant and Harry Suhl, Thin-film magnetic patterns in an external field, Appl. Phys. Lett.
**54**, 2224 (1989). - Paul Bryant and Harry Suhl, Micromagnetics below saturation, J. Appl. Phys.
**66**, 4329 (1989). - Paul Bryant and Carson Jeffries, Spin-Wave Nonlinear Dynamics in an Yttrium Iron Garnet Sphere, Phys. Rev. Lett.
**60**, 1185 (1988). - Paul Bryant and Carson Jeffries, Bifurcations of a Forced Magnetic Oscillator near Points of Resonance, Phys. Rev. Lett.
**53**, 250 (1984).

- Paul Bryant (C) 1987, Studies of Nonlinear and Chaotic Phenomena in Solid State Systems: [Abstract] [Thesis]

- Paul Bryant (C) 2009-2011, LyapOde (Version 6): for calculation of all Lyapunov exponents when the differential equations are known, using the QR decomposition method. Can also calculate the conditional Lyapunov exponents for coupled identical systems. Includes source code written in "C". The software can be compiled for running on Windows, Mac, or Linux/Unix systems. Includes the equations for several systems (Lorenz, Rossler, etc.) and documentation on how to create and compile software for additional systems of the user's choice.
- Paul Bryant (C) 1990, 1993, 2014, Lyap (Current Version 2.1) or Lyap (1990 Version 1.0): for calculation of Lyapunov exponents from time series data. The Lyapunov Exponent calculation is greatly enhanced by using a power series expansion instead of a simple linear function to characterize the mapping of displacement vectors from one time step to the next. Note that calculation of negative exponents from chaotic experimental data is extremely sensitive to noise. This is because the data is confined to a strange attractor which extends very little in directions associated with negative exponents. The software also tries to quantify the extension or degree of singularity of the data set in these directions. Use the ODE code if the equations are known. Includes documentation and test data from the Lorenz system. Includes source code written in Fortran 77. The software can be compiled for running on Windows, Mac, or Linux/Unix systems. Recently compiled succesfully on Windows using the g95 fortran compiler (to install: download, change extension to exe, run).
- Paul Bryant (C) 2008, DataSync (Version 58): for determining optimal parameters for a model of a physical system by fitting the model to one or more experimental time series. The optimization process is enhanced by using synchronization techniques, similar to the methods used to synchronize chaotic systems. A single shooting approach is used in which the initial conditions of the model variables are treated like additional parameters. User can select from several known algorithms to find the parameters that minimize a cost function that characterizes the difference between the model and the time series. The software allows for optional drive signals such as neuron injection current. Multiple datasets and multiple trials can be analyzed simultaneously. Detailed documentation is provided. A variety of model equations are provided for neurons, chaotic systems, etc. Some sample data and configuration files are also provided. Includes source code written in "C". The software can be compiled for running on Windows, Mac, or Linux/Unix systems.