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- Till D. Frank
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2005

We study time-delayed stochastic systems that can be described by means of so-called delay Fokker-Planck equations. Using Novikov's theorem, we first show that the theory of delay Fokker-Planckâ€¦ (More)

- Till D. Frank
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2005

We study nonlinear stochastic systems with time-delayed feedback using the concept of delay Fokker-Planck equations introduced by Guillouzic, L'Heureux, and Longtin. We derive an analyticalâ€¦ (More)

- Till D. Frank
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2002

Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived forâ€¦ (More)

- Michael T. Turvey, Steven J. Harrison, Till D. Frank, Claudia Carello
- Journal of experimental psychology. Humanâ€¦
- 2012

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary gaits are characterizedâ€¦ (More)

- Axel Hutt, Till D. Frank
- 2005

This work studies the stability and the stochastic properties of neural activity evoked by external stimulation. The underlying nonlocal model describes the spatiotemporal response dynamics of neuralâ€¦ (More)

- S. Mongkolsakulvong, P. Chaikhan, Till D. Frank
- 2017

We study the emergence of oscillatory self-sustained behavior in a nonequilibrium Nambu system that features an exchange between different kinetical and potential energy forms. To this end, we studyâ€¦ (More)

- S. Kim, Jeffrey M Gordon, Till D. Frank
- Open Syst. Inform. Dynam.
- 2015

- D. G. Dotov, S. Kim, Till D. Frank
- Biosystems
- 2015

We derive explicit expressions for the non-equilibrium thermodynamical variables of a canonical-dissipative limit cycle oscillator describing rhythmic motion patterns of active systems. Theseâ€¦ (More)

A novel experimental paradigm and a novel modelling approach are presented to investigate oscillatory human motor performance by means of a key concept from condensed matter physics, namely,â€¦ (More)

- Till D. Frank
- Journal of biological physics
- 2011

We demonstrate that elementary biochemical reactions defined by mass-action kinetics satisfy a particular Nambu structure. To this end, we express biochemical reaction equations in terms of Nambuâ€¦ (More)