Zobrazeno 1 - 10
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pro vyhledávání: '"Kalies, William"'
Autor:
Kalies, William, Vandervorst, Robert
For an arbitrary dynamical system there is a strong relationship between global dynamics and the order structure of an appropriately constructed Priestley space. This connection provides an order-theoretic framework for studying global dynamics. In t
Externí odkaz:
http://arxiv.org/abs/2407.14359
Autor:
Batko, Bogdan, Gameiro, Marcio, Hung, Ying, Kalies, William, Mischaikow, Konstantin, Vieira, Ewerton
We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic behavior with rigorous probability guarantees. More precisely, the spar
Externí odkaz:
http://arxiv.org/abs/2206.13779
Deep learning models evolve through training to learn the manifold in which the data exists to satisfy an objective. It is well known that evolution leads to different final states which produce inconsistent predictions of the same test data points.
Externí odkaz:
http://arxiv.org/abs/2106.07683
Publikováno v:
In Journal of Differential Equations 15 September 2023 367:124-198
The theory of bounded, distributive lattices provides the appropriate language for describing directionality and asymptotics in dynamical systems. For bounded, distributive lattices the general notion of `set-difference' taking values in a semilattic
Externí odkaz:
http://arxiv.org/abs/1911.09382
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a challenge i
Externí odkaz:
http://arxiv.org/abs/1909.08809
We develop a validated numerical procedure for continuation of local stable/unstable manifold patches attached to equilibrium solutions of ordinary differential equations. The procedure has two steps. First we compute an accurate high order Taylor ex
Externí odkaz:
http://arxiv.org/abs/1706.10107
Publikováno v:
In Journal of Neuroscience Methods 1 June 2020 339
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The algebraic structure of the attractors in a dynamical system determine much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods, which can in
Externí odkaz:
http://arxiv.org/abs/1409.5405