Slow invariant manifolds as curvature of the flow of dynamical systems [PDF]
, 2014 Considering trajectory curves, integral of n-dimensional dynamical systems, within the framework of Differential Geometry as curves in Euclidean n-space, it will be established in this article that the curvature of the flow, i.e.
Chua, Leon +2 more
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Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem. [PDF]
Physical Review E, 2020 This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations.
Lyudmila Grigoryeva +2 more
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On dynamical properties of general dynamical systems and differential inclusions
Journal of Mathematical Analysis and Applications, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaoxian Zhang, Desheng Li
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Lectures on Structural Stability in Dynamics
, 2017 These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable).
Berger, Pierre
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Least Squares Shadowing method for sensitivity analysis of differential equations [PDF]
, 2017 For a parameterized hyperbolic system $\frac{du}{dt}=f(u,s)$ the derivative of the ergodic average $\langle J \rangle = \lim_{T \to \infty}\frac{1}{T}\int_0^T J(u(t),s)$ to the parameter $s$ can be computed via the Least Squares Shadowing algorithm (LSS).
Blonigan, Patrick J. +3 more
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Designing self-assembling kinetics with differentiable statistical physics models
Proceedings of the National Academy of Sciences of the United States of America, 2021 Significance Engineering at the nanoscale is rich and complex: researchers have designed small-scale structures ranging from smiley faces to intricate sensors.
C. Goodrich +4 more
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Lyapunov exponent for Lipschitz maps
, 2018 It is well-known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose an alternative definition of Lyapunov exponent in terms of Lipschitz maps, which are not necessarily differentiable.
La Guardia, Giuliano G. +1 more
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Input-to-State Safety With Control Barrier Functions [PDF]
, 2018 This letter presents a new notion of input-to-state safe control barrier functions (ISSf-CBFs), which ensure safety of nonlinear dynamical systems under input disturbances.
Ames, Aaron D., Kolathaya, Shishir
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Random Dynamical Systems for Stochastic Evolution Equations Driven by Multiplicative Fractional Brownian Noise with Hurst Parameters H ∈ (1/3, 1/2] [PDF]
SIAM Journal on Applied Dynamical Systems, 2015 We consider the stochastic evolution equation $du=Audt+G(u)d\omega,\quad u(0)=u_0$ in a separable Hilbert space $V$. Here $G$ is supposed to be three times Frechet-differentiable and $\omega$ is a trace class fractional Brownian motion with Hurst ...
M. Garrido-Atienza, K. Lu, B. Schmalfuß
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An Analytical Construction of the SRB Measures for Baker-type Maps [PDF]
, 1998 For a class of dynamical systems, called the axiom-A systems, Sinai, Ruelle and Bowen showed the existence of an invariant measure (SRB measure) weakly attracting the temporal average of any initial distribution that is absolutely continuous with respect
Besicovitch A. S. +9 more
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