PUBLICATIONS

(Not a complete listing)

Books

T. Frank, Determinism and self-organization of human perception and performance (Springer, Berlin, 2019)
ISBN 978-3-030-28820-4

T. D. Frank, Nonlinear Fokker-Planck equations: Fundamentals and Applications (Springer, Berlin, 2005)
ISBN 3-540-21264-7

Articles

******************** 2012 **************

  • Richardson, M.J., Garcia, R.L., Frank, T.D., Gregor, M., Marsh, K.L. (2012). Measuring group synchrony: a cluster-phase method for analyzing multivariate movement time series. Frontiers in Physiology, 3: article 405 (10 pages)
  • Frank, T.D., Cheong, A., Okada-Hatakeyama, M., Kholodenko, B.N. (2012). Catching transcriptional regulation by thermostatistical modeling. Physical Biology, 9: 045007
  • Frank, T.D. Silva, P.L., Turvey, M. T. (2012). Symmetry axiom of Haken-Kelso-Bunz coordination dynamics revisited in the context of cognitive activity. Journal of Mathematical Psychology, 56: 149-165
  • Frank, T. D., Blau, J. J. C., Turvey, M. T. (2012). Symmetry breaking analysis of prism adaptation’s latent aftereffect. Cognitive Science, 36: 674-697
  • Frank, T.D. Carmody, A.M., Kholodenko, B.N. (2012). Versatility of cooperative transcriptional activation: a thermodynamical modeling analysis for greater-than-additive and less-than-additive effect. PLoS One, 7: e34439 (15 pages)
  • Bruning, U., Fitzpatrick, S. F., Birtwistle, M., Frank, T., Taylor, C. T., Cheong, A. (2012). NFkappaB and HIF display synergistic behavior during hypoxic stimulation. Cellular and Molecular Life Science, 69: 1319-1329
  • Mongkolsakulvong, S., Chaikan P., Frank, T.D. (2012). Oscillatory nonequilibrium Nambu systems: the canonical-dissipative Yamaleev oscillator. European Physical
    Journal B, 85:     90 (10 pages)
  • Isenhower, R.W., Kant, V., Frank, T. D., Pinto, C. M. A., Carello, C., Turvey, M. T. (2012). Equivalence of human odometry by walk and run is indifferent to self-selected speed. Journal of Motor Behavior, 44: 47-52

******************** 2011 **************

  • Dotov, D. G., Frank, T. D. (2011). From the W-method to the canonical-dissipative method for studying uni-manual rhythmic behavior. Motor Control, 15: 550-567
  • Frank T. D. (2011). Nonlinear physics approach to DNA cross-replication: marginal stability, generalized logistic growth, and impacts of degradation.Physics Letters A, 375: 3851-3857
  • Frank, T. D. (2011). Stochastic processes and mean field systems defined by nonlinear Markov chains: an illustration for a model of evolutionary population dynamic.Brazilian Journal of Physics, 41: 129-134
  • Frank T. D. (2011). Fractional Brownian motion analysis does not provide evidence for neurophysiological feedback mechanisms: a comment on ‘White matter hyperintensities and dynamics of postural control’. Magnetic Resonance Imaging, 29: 887-888
  • Frank T. D. (2011). Rate of entropy production as a physical selection principle for mode-mode transitions in non-equilibrium systems: with an application to a non-algorithmic dynamic message buffer. European Journal of Scientific Research, 54: 59-74
  • Frank T. D. (2011). Collective behavior of biophysical systems with thermodynamic feedback loops: a case study for a nonlinear Markov model — the Takatsuji system.Modern Physics Letters B, 25: 551-568
  • Frank T. D. (2011). Multistable selection equations of pattern formation type in the case of inhomogeneous growth rates: with applications to two-dimensional assignment problems. Physics Letters A, 375: 1465-1469

******************** 2010 **************

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  • Frank T. D. (2010). Comment on “Dynamic analysis of postural profiles in quiet stance on carpets through fractional Brownian Motion”.Textile Research Journal, 80: 2115-2116

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  • Frank T. D., Richardson, M.J. (2010). On a test statistic for the Kuramoto order parameter of synchronization: with an illustration for group synchronization during rocking chairs. Physica D, 239:2084-2092

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  • Frank T. D. (2010). A Fokker-Planck approach to canonical-dissipative Nambu systems: with an application to human motor control during dynamic haptic perception.Physics Letters A, 374: 3136-3142

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  • Frank, T.D. (2010). Active systems with Nambu dynamics: with a applications to rod wielding for haptic length perception and self-propagating systems on two-spheres. European Physical Journal B, 74: 195-203

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  • Mongkolsakulvong, S., Frank, T.D. (2010). Canonical-dissipative limit cycle oscillators with a short-range interaction in phase space.Condensed Matter Physics, 13: 13001 (18 pages)

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  • Bonnet, C.T., Kinsella-Shaw, J.M., Frank, T.D., Bubela, D., & Turvey, M.T. (2010). Deterministic and stochastic postural processes: effects of age, task, environment.Journal of Motor Behavior, 42: 85-97

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******************** 2009 **************

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  • Frank, T.D. (2009). On a multistable competitive network model in the case of an inhomogeneous growth rate spectrum: with an application to priming.Physics Letters A, 373: 4127-4133

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  • Frank, T.D. (2009). Deterministic and stochastic components of nonlinear Markov models with an application to decision making during the bailout votes 2008 (USA).European Physical Journal B, 70: 249-255

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  • Frank, T.D. (2009). Chaos from nonlinear Markov processes: why the whole is different from the sum of its parts.Physica A, 388: 4241-4247

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  • Frank, T.D., Mongkolsakulvong, S. (2009). Parametric solution methods for self-consistency equations and order parameter equations derived from nonlinear Fokker-Planck equations.Physica D, 238: 1186-1196

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  • Frank, T.D. (2009). Nonextensive cutoff distributions of postural sway for the old and the youngPhysica A, 388: 2503-2510

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  • Frank, T.D., Blau. J.J.C., Turvey, M.T. (2009). Nonlinear attractor dynamics in the fundamental and extended prism adaptation paradigm,Physics Letters A, 373: 1022-1030

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  • Stepp, N., Frank, T.D. (2009). A data analysis method for decomposing synchronization variability of anticipatory systems into stochastic and deterministic components,European Physical Journal B, 67: 251-257

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******************** 2008 **************

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  • Frank, T.D. (2008). Fokker-Planck equations are more than just partial differential equations: a comment on a study by Dehghan and Tatari (Phys. Scr. 74:2006: 310),Physica Scripta , 78: 067001

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  • Frank, T.D. (2008). Markov chains of nonlinear Markov processes and an application to a winner-takes-all model for social conformity,Journal of Physics A, 41: 282001

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  • Frank, T.D., Mongkolsakulvong, S. (2008). A nonextensive thermostatistical approach to the Haissinski theory of accelerator beams, Physica A , 387: 4828-4838( Erratum).

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  • Frank, T.D., Patanarapeelert, K., Beek, P.J. (2008) Portfolio theory of optimal isometric force production: variability predictions and nonequilibrium fluctuation-dissipation theorem, Physics Letters A, 372: 3562-3568

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  • Frank, T.D., Michelbrink, M., Beckmann, H., Schöllhorn, W.I. (2008). On a quantitative dynamical systems approach to differential learning: self-organization principle and order parameter equations,Biological Cybernetics, 98: 19-31.

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  • Frank, T.D. (2008). Green functions and Langevin equations for nonlinear diffusion equations: a comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.Physica A, 387: 773-778

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******************** 2007 **************

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  • Wilmer, A., Frank, T.D., Beek, P.J., Friedrich, R. (2007). A data-analysis method for identifying differential effects of time-delayed feedback forces and periodic driving forces in stochastic systems, European Physical Journal B, 60: 203-215

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  • Frank, T.D. (2007). Towards a time-continuous MA(1) model: application to stock index returns, Nonlinear phenomena in complex systems, 10(3): 256-263.

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  • Müller, H., Frank, T.D., Sternad, D. (2007). Variability, covariation and invariance with respect to coordinate systems in motor control: reply to Smeets and Louw (2007). Journal of
    Experimental Psychology: Human Perception and Performance     :33: 250-255.

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  • Frank, T.D. (2007). Exact solutions and Monte Carlo simulations of self-consistent Langevin equations: a case study for the collective dynamics
    of stock prices. International Journal of Modern Physics B, 21: 1099-1112.

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  • Frank, T.D. (2007). A mini-tutorial on measure-valued Markov processes and nonlinear martingale problems, Physica A, 382: 453-464, 2007

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  • Mongkolsakulvong, S., Frank, T.D., Tang, I.M. (2007). Phenomenological generalization of the Maier-Saupe theory for nematic liquid crystals in the framework of the dynamical mean field approach, Phase Transitions, 80: 967-980.

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******************** 2006 **************

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  • Frank, T.D., Friedrich, R., Beek, P.J. (2006). Stochastic order parameter equation of isometric force production revealed by drift-diffusion estimates. Physical Review E, 74: 051905.

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  • Patanarapeelert, K., Frank, T.D., Friedrich, R., Beek, P.J.,Tang I.M. (2006). A data analysis method for identifying deterministic components of stable and unstable time-delayed
    systems with colored noise. Physics Letters A, 360: 190-198.

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  • Frank, T.D. (2006). Smoluchowski approach to nonlinear Vlasov-Fokker-Planck equations: stability analysis of beam dynamics and Haissinski
    theory. Physical Review ST-AB, 9: 084401.

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  • Patanarapeelert, K., Frank, T.D., Friedrich, R., Beek, P.J.,Tang, I.M. (2006). Theoretical analysis of destabilization resonances in time-delayed stochastic second order dynamical
    systems and some implications for human motor control. Physical Review E, 73: 021901.

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  • Frank, T.D. (2006). Time-dependent solutions for stochastic systems with delays: perturbation theory and applications to financial physics. Physics Letters A, 357: 275-283.

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******************** 2005 **************

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  • Frank, T.D., Friedrich, R. (2005). Estimating the nonextensivity of systems from experimental data: a nonlinear diffusion equation approach.Physica A, 347: 65-76.

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  • Frank, T.D., Patanarapeelert, K., Tang, I.M.(2005). Delay- and noise-induced transitions: a case study for a Hongler model with time delay.Physics Letters A, 339: 246-251.

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  • Frank, T.D., Friedrich, R., Beek, P.J. (2005). Identifying and comparing states of time-delayed systems: phase diagrams and applications to human movements.Physics Letters A, 338: 74-80.

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  • Frank, T.D. (2005). Short-time correlations of many-body systems described by nonlinear Fokker-Planck equations and Vlasov-Fokker-Planck equations.Physics Letters A 337:224-234.

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  • Frank, T.D., Friedrich, R., Beek, P.J. (2005). Time series analysis for multivariate time-delayed systems with noise: applications to laser physics and human movements.Stochastics and dynamics, 5(2): 297-306.

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  • Frank, T.D. (2005). On the characterization of nanoporous materials by means of empirical and intrinsic transport coefficients.Science and Technology of Advanced Materials, 6: 221-223.

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  • Frank, T. D. (2005). On the Maier-Saupe model of liquid crystals: isotropic-nematic phase transitions and second order statistics studied by Shiino’s perturbation theory and strongly nonlinear Smoluchowski equations.Physical Review E, 72: 041703( Erratum).

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  • Frank, T.D. (2005). Delay Fokker-Planck equations, Novikov’s theorem, and Boltzmann distributions as small delay approximations.Physical Review E, 72: 011112.

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  • Frank T.D. (2005). Delay Fokker-Planck equations, perturbation theory, and data analysis for nonlinear stochastic systems with time delays.Physical Review E, 71:031106.

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  • Patanarapeelert, K., Frank, T.D., Friedrich, R., Tang, I.M. (2005). On reducible nonlinear time-delayed stochastic systems: fluctuation-dissipation relations, transitions to bistability, and secondary bifurcations to non-stationarityJournal of Physics A, 38: 10069-10083.

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  • Frank, T.D. (2005). Stationary distributions of stochastic processes described by a linear neutral delay differential equation.Journal of Physics A, 38: L485-L490.

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  • Frank, T.D.(2005). Modelling the stochastic single particle dynamics of relativistic fermions and bosons using nonlinear drift-diffusion equations. Mathematical and Computer Modelling,42: 1057-1062.

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  • Hutt, A., Frank, T.D. (2005). Stability, critical fluctuations and $1/f^\alpha$-activity of neural fields involving transmission delays.Acta Physica Polonica B, 108: 1021-1040.

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******************** 2004 **************

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  • Frank T.D. (2004). Autocorrelation functions of nonlinear Fokker-Planck equations.European Physics Journal B, 37: 139-142.

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  • Frank T.D. (2004). Asymptotic properties of nonlinear diffusion, nonlinear drift-diffusion, and nonlinear reaction-diffusion equations. Annalen der Physik, 13: 461-469.

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  • Frank T.D. (2004). Analytical results for fundamental time-delayed feedback systems subjected to multiplicative noise.Physical Review E, 69: 061104.

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  • Frank T.D. (2004). On a nonlinear master equation and the Haken-Kelso-Bunz model.Journal of Biological Physics, 30: 139-159.

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  • Frank T.D. (2004). Complete description of a generalized Ornstein-Uhlenbeck process related to the nonextensive Gaussian entropy.Physica A, 340:251-256.

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  • Frank T.D. (2004). Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations.Physica A, 331: 391-408.

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  • Frank T.D. (2004). Dynamic mean field models: H-theorem for stochastic processes and basins of attraction of stationary processes.Physica D, 195: 229-243.

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  • Frank T.D. (2004). Stability analysis of stationary states of mean field models described by Fokker-Planck equations.Physica D, 189: 199-218.

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  • Frank T.D. (2004). Fluctuation-dissipation theorems for nonlinear Fokker-Planck equations of the Desai-Zwanzig type and Vlasov-Fokker-Planck equations.Physics Letters A, 329: 475-485.

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******************** 2003 **************

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  • Frank T.D. (2003). A note on the Markov property of stochastic processes described by nonlinear Fokker-Planck equations.Physica A, 320:204-210.

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  • Frank T.D., Beek P.J., Friedrich R. (2003). Fokker-Planck perspective on stochastic delay systems: exact solutions and data analysis of biological systems.Physical Review E, 68: 021912.

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  • Bödeker H.U., Röttger M.C., Liehr A.W., Frank T.D., Friedrich R., Purwins H.G. (2003). Noise-covered drift bifurcation of dissipative solitons in a planar gas-discharge system.Physical Review E, 67: 056220.

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******************** 2002 **************

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  • Frank T.D. (2002). On a general link between anomalous diffusion and nonextensivity.Journal of Mathematical Physics, 43:344-350.

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  • Frank T.D. (2002). Generalized Fokker-Planck equations derived from generalized linear nonequilibrium thermodynamics.Physica A, 310: 397-412.

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  • Frank T.D. (2002). Multivariate Markov processes for stochastic systems with delays: Application to the stochastic Gompertz model with delay.Physical Review E, 66: 011914.

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  • Frank T.D., Daffertshofer A., Beek P.J. (2002). Impacts of statistical feedback on the flexibility-accuracy trade-off of biological systems.Journal of Biological Physics, 28: 39-54.

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  • Frank T.D. (2002). Stability analysis of mean field models described by Fokker-Planck equations.Annalen der Physik, 11:707-716.

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  • Frank T.D., Plastino, A.R. (2002). Generalized thermostatistics based on the Sharma-Mittal entropy and escort mean values.European Physical Journal B, 30: 543-549.

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******************** 2001 **************

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  • Frank T.D., Beek P.J. (2001). Stationary solutions of linear stochastic delay differential equations: Applications to biological systems.Physical Review E, 64: 021917.

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  • Frank T.D., Daffertshofer A., Beek P.J. (2001). Multivariate Ornstein-Uhlenbeck processes with mean field dependent coefficients: Applications to postural sway.Physical Review E, 63: 011905.

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  • Frank T.D., Daffertshofer A., Peper C.E., Beek P.J., Haken H. (2001). H-theorem for a mean field model describing coupled oscillator systems under external forces.Physica D, 150: 219-236.

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  • Frank T.D. (2001). A Langevin approach for the microscopic dynamics of nonlinear Fokker-Planck equations.Physica A, 301: 52-62.

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  • Frank T.D., Daffertshofer A. (2001). H-theorem for nonlinear Fokker-Planck equations related to generalized thermostatistics.
    Physica A, 295: 455-474.

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  • Frank T. D. and Daffertshofer A. (2001). Multivariate nonlinear Fokker-Planck equations and generalized thermostatistics.Physica A, 292: 392-410.

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  • Frank T. D., Daffertshofer A., and Beek P. J. (2001). Interpreting screw displacement apparent motion as a self-organizing process.Behavioral and Brain Sciences, 24: 668-669.

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******************** 2000 **************

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  • Frank, T.D., Daffertshofer, A., Peper, C.E., Beek, P.J., Haken, H.(2000). Towards a comprehensive theory of brain activity: coupled oscillator systems under external forces.Physica D, 144: 62-86.

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  • Frank, T.D., Daffertshofer, A. (2000). Exact time-dependent solutions of the Renyi Fokker-Planck equation and the Fokker-Planck equations related to
    the entropies proposed by Sharma and Mittal.Physica A, 285: 129-144.

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  • Daffertshofer, A., Frank, T.D., Peper, C.E., Beek, P.J. (2000). Three pertinent issues in the modeling of brain activity: Nonlinearities,
    time scales and neural underpinnings.Behavioral and Brain Sciences, 23:400-401.

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  • Daffertshofer A., Peper C.E., Frank T.D., Beek P.J. (2000). Spatio-temporal patterns of encephalographic signals during polyrhythmic tapping.Human Movement Science, 19: 474-498.

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******************** 1999 **************

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  • Frank, T.D., Daffertshofer, A. (1999). Nonlinear Fokker-Planck equations whose stationary solutions make entropy-like functionals stationaryPhysica A, 272: 497-508.
    ( Erratum).

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  • Frank, T.D., Daffertshofer, A., Beek, P.J., Haken, H. (1999). Impacts of noise on a field theoretical model of the human brain. Physica D, 127: 233-249.