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Robust non-computability of dynamical systems and computability of robust dynamical systems [PDF]
Logical Methods in Computer ScienceIn this paper, we examine the relationship between the stability of the dynamical system $x^{\prime}=f(x)$ and the computability of its basins of attraction.
Daniel S. Graça, Ning Zhong
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Perturbed Basins of Attraction [PDF]
Mathematische Annalen, 2006 Let F be an automorphism of C^k which has a fixed point. It is well known that the basin of attraction is biholomorphically equivalent to C^k. We will show that the basin of attraction of a sequence of automorphisms is also biholomorphic to C^k if all the automorphisms are small perturbations of the original map F.
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Basins of attraction on random topography [PDF]
Physical Review E, 2001 We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to the curvature of the contour line divided by the local slope.
Schorghofer, N., Rothman, D. H.
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Complexity, 2021 In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically.
Yélomè Judicaël Fernando Kpomahou +3 more
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Basins of attraction in human balance [PDF]
The European Physical Journal Special Topics, 2017 Falls are a recognized risk factor for unintentional injuries among older adults, accounting for a large proportion of fractures, emergency department visits, and urgent hospitalizations. Human balance and gait research traditionally uses linear or qualitative tests to assess and describe human motion; however, human motion is neither a simple nor a ...
Victoria A, Smith +2 more
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Multistability in a Circulant Dynamical System
Communications in Advanced Mathematical Sciences, 2023 In this paper we report on a two parameter four-dimensional dynamical system with cyclic symmetry, namely a circulant dynamical system. This system is a twelve-term polynomial system with four cubic nonlinearities.
Paulo Rech
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Newton’s method’s basins of attraction revisited [PDF]
Applied Mathematics and Computation, 2009 In this paper, we revisit the chaotic number of iterations needed by Newton's method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in the simple algorithm the presence and the position of the convergent regions, i.e.
Susanto, H., Karjanto, N.
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Random Walk over Basins of Attraction to Construct Ising Energy Landscapes [PDF]
, 2011 An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal averages over each
Qing Zhou, Y. F. Atchade
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Basins of attraction for chimera states [PDF]
New Journal of Physics, 2016 Please see Ancillary files for the 4 supplementary videos including description (PDF)
Martens, Erik Andreas +2 more
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Computation and verification of Lyapunov functions [PDF]
, 2015 Lyapunov functions are an important tool to determine the basin of attraction of equilibria in Dynamical Systems through their sublevel sets. Recently, several numerical construction methods for Lyapunov functions have been proposed, among them the RBF ...
Dellnitz M. +6 more
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