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matcont: A matlab package for numerical bifurcation analysis of ODEs

by A. Dhooge, W. Govaerts, Yu. A. Kuznetsov - ACM TOMS , 2003
"... the interactive numerical study of dynamical systems. It allows to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles, fold,flip and torus bifurcation points of limit cycles. The matcont gui makes the standard Matlab ODE Suite in ..."
Abstract - Cited by 96 (4 self) - Add to MetaCart
interactively available and provides computational and visualization tools. matcont uses the Matlab symbolic toolbox whenever it is available; higher order derivatives are important e.g. in the computation of normal forms. The sparsity of the discretized systems for the computation of limit cycles

BIFURCATION ANALYSIS OF PERIODIC ORBITS OF MAPS IN MATLAB

by W. Govaerts, R. Khoshsiar Ghaziani, Yu. A. Kuznetsov, H. G. E
"... Abstract. We discuss new and improved algorithms for the bifurcation analysis of fixed points and periodic orbits (cycles) of maps and their implementation in matcont, a matlab toolbox for continuation and bifurcation analysis of dynamical systems. This includes the numerical continuation of fixed p ..."
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of codim 1 and 2, the critical normal form coefficients are computed, both numerically with finite directional differences and using symbolic derivatives of the original map. Using a parameter-dependent center manifold reduction, explicit asymptotics are derived for bifurcation curves of double

Computational bifurcation and stability studies of the 8:1 thermal cavity problem

by Andrew G. Salinger, Richard B. Lehoucq, Roger P. Pawlowski, John N. Shadid - Int. J. Numer Methods Fluids
"... Stability analysis algorithms coupled with a robust Newton-Krylov steady state iterative solver are used to understand the behavior of the 2D model problem of thermal convection in a 8:1 differentially heated cavity. Parameter continuation methods along with bifurcation and linear stability analysis ..."
Abstract - Cited by 7 (4 self) - Add to MetaCart
Stability analysis algorithms coupled with a robust Newton-Krylov steady state iterative solver are used to understand the behavior of the 2D model problem of thermal convection in a 8:1 differentially heated cavity. Parameter continuation methods along with bifurcation and linear stability

Instabilities in spatially extended

by Martin Baurmann A, Thilo Gross B, Ulrike Feudel A
"... predator-prey systems: Spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations ..."
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predator-prey systems: Spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations

Amplitude equations close to a triple-(+1) bifurcation point ofD4-symmetric periodic orbits inO(2)-equivariant systems, Discrete Contin

by Marta Net, Jose ́ M. Vega - Dyn. Syst. B , 2006
"... (Communicated by Shouhong Wang) Abstract. A two-dimensional thermal convection problem in a circular an-nulus subject to a constant inward radial gravity and heated from the inside is considered. A branch of spatio-temporal symmetric periodic orbits that are known only numerically shows a multi-crit ..."
Abstract - Cited by 5 (1 self) - Add to MetaCart
-critical codimension-two point with a triple +1-Floquet multiplier. The weakly nonlinear analysis of the dynamics near such point is performed by deriving a system of amplitude equations us-ing a perturbation technique, which is an extension of the Lindstedt-Poincaré method, and solvability conditions. The results

Research Article Bifurcation and dynamics of a normal form map

by Turk J Math, Reza Khoshsiar Ghaziani
"... Abstract: This paper investigates the dynamics and stability properties of a so-called planar truncated normal form map. This kind of map is widely used in the applied context, especially in normal form coecients of n-dimensional maps. We determine analytically the border collision bifurcation curve ..."
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to stable attractors called invariant closed curves, and chaos, where dynamics of the system change erratically. Our study is based on the numerical continuation method under variation of 1 and 2 parameters and computation of dierent bifurcation curves of the system and its iterations. For the all

Applied and Computational Harmonic Analysis

by unknown authors
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution

Theory of Computing Systems

by M. Mitzenmacher
"... Abstract. It is well known that simple randomized load balancing schemes can balance load effectively while incurring only a small overhead, making such schemes appealing for practical systems. In this paper we provide new analyses for several such dynamic randomized load balancing schemes. Our work ..."
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that using d = 2 choices yields an exponential improvement in the expected time a customer spends in the system over d = 1 choice (simple random selection) in equilibrium. Here we examine several variations, including constant service times and threshold models, where a customer makes up to d successive

Volume I: Computer Science and Software Engineering

by Ioannis Z. Emiris, Victor Y. Pan, Elias P. Tsigaridas, Allen Tucker, Teo Gonzales, Jorge L. Diaz-herrera, Ioannis Z. Emiris, Victor Y. Pan, Elias P. Tsigaridas , 2013
"... Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations in Sc ..."
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Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations

Multi-loop Position Analysis via Iterated Linear Programming

by unknown authors
"... Abstract — This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology, ..."
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. The method is conceptually simple, geometric in nature, and easy to implement, yet it provides solutions at the desired accuracy in short computation times. I.
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