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Reconstructing Waddington's Landscape from Data

Cislo DJ, Delás MJ, Briscoe J, Siggia ED.   +3 more
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A mechanistic theory of planning in prefrontal cortex

Jensen KT, Doohan P, Sablé-Meyer M, Reinert S, Baram A, Akam T, Behrens TEJ.   +6 more
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Exponential Attractors in Banach Spaces

Journal of Dynamics and Differential Equations, 2001
Let \(E\) be a Banach space, \(U\subset E\) an open set and \(S:U\rightarrow E\) a \(C^1\)-map. The authors consider the discrete dynamical system (DS) \(\{S^n\}_{n=1}^{\infty}\) generated by \(S\), extending the theory of exponential attractors from such DS in Hilbert space [\textit{A. Eden, C. Foias, B. Nicolaenko} and \textit{R.
Dung, L., Nicolaenko, B.
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Exponential Attractors in Generalized Relativistic Billiards

Communications in Mathematical Physics, 2004
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Deryabin, M. V., Pustyl'nikov, L. D.
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Finite‐dimensional attractors and exponential attractors for degenerate doubly nonlinear equations

Mathematical Methods in the Applied Sciences, 2009
AbstractWe consider the following doubly nonlinear parabolic equation in a bounded domain Ω⊂ℝ3:where the nonlinearityfis allowed to have a degeneracy with respect to ∂tuof the form ∂tu|∂tu|pat some pointsx∈Ω.Under some natural assumptions on the nonlinearitiesfandg, we prove the existence and uniqueness of a solution of that problem and establish the ...
Efendiev, M, Zelik, S
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Exponential attractors for a partially dissipative reaction system

Asymptotic Analysis, 1996
After having established the existence of smooth absorbing sets, thanks to suitable a priori estimates, we obtain for a class of partially dissipative reaction systems a property known as squeezing property. This last leads to the existence of exponential attractors for which the fractal dimension is finite.
Fabrie, P., Galusinski, C.
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Exponential attractors for extensible beam equations

Nonlinearity, 1993
The authors transfer ideas and results of the classical theory of dynamical systems for ODE to a class of nonlinear dynamical boundary value problems for PDE which includes equations looking like beam and plate equations. They establish the existence of a compact attractor and some of its properties for this class of systems using energy methods and ...
Eden, A., Milani, A. J.
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Pullback Exponential Attractors for Nonautonomous Reaction–Diffusion Equations

International Journal of Bifurcation and Chaos, 2015
This paper presents a necessary and sufficient condition to prove the existence of the pullback exponential attractor. The asymptotic a priori estimate method is used to produce an abstract result on the existence of the pullback exponential attractor in a strong space without regularity. The established results are illustrated by applying them to the
Yan, Xingjie, Qi, Wei
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Pullback Exponential Attractors for Non-autonomous Lattice Systems

Journal of Dynamics and Differential Equations, 2012
The authors first present some sufficient conditions for the existence and the construction of a pullback exponential attractor for the continuous process (non-autonomous dynamical system) on Banach spaces and weighted spaces of infinite sequences. Then they apply the results to study the existence of pullback exponential attractors for first-order non-
Zhou, Shengfan, Han, Xiaoying
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