Results 261 to 270 of about 15,535 (305)
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On the susceptibility of numerical methods to computational chaos and superstability
Communications in Nonlinear Science and Numerical Simulation, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
C Varsakelis
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Numerical proof for chemostat chaos of Shilnikov's type
Chaos, 2017A classical chemostat model is considered that models the cycling of one essential abiotic element or nutrient through a food chain of three trophic levels. The long-time behavior of the model was known to exhibit complex dynamics more than 20 years ago. It is still an open problem to prove the existence of chaos analytically.
Bo Deng, Maoan Han, Sze-Bi Hsu
exaly +4 more sources
Numerical research on chaos control
The 2nd International Conference on Information Science and Engineering, 2010In this paper, the numerical simulation method is applied to investigate the control for a given chaotic system. In order to obtain a better understanding of the relationship between the Lyapunov exponents and evolution of chaos, a stable Duffing system is examined.
exaly +2 more sources
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal of Scientific Computing, 2004Summary: This paper gives an overview of the use of polynomial chaos (PC) expansions to represent stochastic processes in numerical simulations. Several methods are presented for performing arithmetic on, as well as for evaluating polynomial and nonpolynomial functions of variables represented by PC expansions.
Bert Debusschere +2 more
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Numerical approximation of homoclinic chaos
Numerical Algorithms, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Beyn, Wolf-Jürgen, Kleinkauf, J. M.
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NUMERICAL TREATMENT OF EDUCATIONAL CHAOS OSCILLATOR
International Journal of Bifurcation and Chaos, 2007A mathematical model of a recently suggested chaos oscillator for educational purposes is treated and numerical results are presented. Bifurcation diagrams, phase portraits, power spectra, Lyapunov exponents are simulated. In addition, the Feigenbaum number is estimated.
Arünas Tamasevicius +4 more
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A numerical study of chaos in a reaction‐diffusion equation
Numerical Methods for Partial Differential Equations, 1985AbstractA study is made using numerical experiments to see the effect of the parameters in the explicit Euler‐discretized form of a one‐dimensional, nonlinear, reaction‐diffusion equation. Based on a series of these experiments, one of the main results obtained is that diffusion, which is usually perceived as having a stabilizing effect, is able to ...
Mitchell, A. R., Bruch, John C. jun.
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Numerically induced chaos in the nonlinear Schrödinger equation
Physical Review Letters, 1989The cubic nonlinear Schr\"odinger equation and some of its discretizations, one of which is integ- rable, are studied. Apart from the integrable version the discretizations produce chaotic solutions for intermediate levels of mesh (mode) refinement. Chaos disappears when the discretization is fine enough and convergence to a quasiperiodic solution is ...
, Herbst, , Ablowitz
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Numerical chaos, roundoff errors, and homoclinic manifolds
Physical Review Letters, 1993The focusing nonlinear Schr\"odinger equation is numerically integrated over moderate to long time intervals. In certain parameter regimes small errors on the order of roundoff grow rapidly and saturate at values comparable to the main wave. Although the constants of motion are nearly preserved, a serious phase instability (chaos) develops in the ...
, Ablowitz, , Schober, , Herbst
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Scaling Analysis at Transition of Chaos Driven by Euler’s Numerical Algorithm
International Journal of Bifurcation and Chaos, 2023Chaos is a nonlinear phenomenon that reveals itself everywhere in nature and in many fields of science. It has gained increasing attention from researchers and scientists over the last two decades. In this article, the nature of the fixed and periodic states are examined for a discrete two-parameter map; a composition of Euler’s numerical map and the ...
Jinde Cao, Ashish
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