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The modeling work of cognitive neuroscientists such as Francisco Varela and Walter Freeman seeks to explain embodied and situated cognition in terms of dynamical systems theory and neurophenomenology, but rejects the idea that the brain uses representations to do so (a position also espoused by Gerhard Werner).
Classical attractors in the well-known dynamical systems of Van der Pol, Beluosov–Zhabotinsky, Lorenz, Rössler, Chua and many others are self-excited attractors and can be obtained numerically, with relative ease, by standard computational procedures described above.
Once, while talking with his mentor, Solomon Lefschetz, Maurício Peixoto commented that no one cared about structural stability of dynamical systems and that was the main problem in working with it.
CAPD library - C++ library for rigorous numerics in dynamical systems and homology computation.
Dynamicism, the application of dynamical systems theory to cognitive science
The perturbation theory of toroidal invariant manifolds of dynamical systems was developed here by academician M. M. Bogolyubov, Yu. O. Mitropolsky, academician of the NAS of Ukraine and the Russian Academy of Sciences, and A. M. Samoilenko, academician of the NAS of Ukraine.
In designing feedback controllers for dynamical systems a variety of modern, multivariable controllers are used.
He was a close friend of Dutch physicist Balthasar van der Pol, whose work on nonlinear self-oscillating dynamical systems (see van der Pol oscillator) he extended and popularized among electrical engineers, mathematicians, and economists.
In the context of general relativity, he is best known for his development (with Stanley Deser and Charles Misner) of the ADM formalism, roughly speaking a way of describing spacetime as space evolving in time, which allows a recasting of Einstein's theory in terms of a more general formalism used in physics to describe dynamical systems, namely the Hamiltonian formalism.
In the context of general relativity, he is best known for his development (with Richard Arnowitt and Charles Misner) of the ADM formalism, roughly speaking a way of describing spacetime as space evolving in time, which allows a recasting Einstein's theory in terms of a more general formalism used in physics to describe dynamical systems, namely the Hamiltonian formalism.
In his first regular academic position at Indiana University, van Gelder was heavily influenced by researchers such as Robert Port, James Townsend, Esther Thelen and Linda B. Smith who were exploring cognition from a dynamical perspective, i.e., applying the tools of dynamical systems to studying cognitive processes.