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Showing 1 to 14 of 14 for “"Numerical Continuation"”.
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Robust design optimization with dynamic constraints using numerical continuation
… and integral constraints. A successive parameter continuation method combined with polynomial chaos expansions is used to locate stationary points. The use of such an expansion provides the benefit of being able to directly drive the mean and variance of a given response function (or an objective …
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On the application of numerical continuation to large-scale dynamical systems
… of novel computational algorithms based on numerical path-following techniques. For all systems investigated in this study, a suitable boundary value problem is formulated and the numerical continuation method is used for covering the parameter space using the software-package coco. In this …
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Bifurcations, Multi-stability, and Localization in Thin Structures
… translations, and compares these results with numerical continuation of a perfectly anisotropic Kirchhoff rod model. It is shown that this naive Kirchhoff rod model works surprisingly well as an organizing framework for thin bands with various widths. Thin sheets prefer to bend rather than to …
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C++ software for computing and visualizing 2-D manifolds using Henderson's algorithm
… Furthermore, its algorithms are based on numerical continuation methods, rather than on subdivision techniques, which allows its practical application to the computation of two-dimensional manifolds in high-dimensional Euclidean spaces. The overall software provides a graphical user …
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Population Dynamics and Pattern Formation in an Info-chemical Mediated Tri-trophic Plankton Model
… and by the addition of resources. Further, a numerical continuation technique was used to determine the existence of multiple stationary patterns.
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Dynamics near discontinuity events in systems with hysteresis and systems with finite state resets
… are shown to agree with results produced using numerical continuation. In addition, we remark on the limitations of the discontinuity mapping analysis and provide suggestions for future work. Specifically, we identify a family of attractors that exist for the AFM model and that warrant further …
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Nonlinear Analysis and Control of Aeroelastic Systems
… and its sensitivities are obtained using numerical continuation methods and harmonic balance methods. It is shown that the developed optimal controller eliminates any existing subcritical LCOs by converting them to supercritical LCOs.
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Natural and artificial orbits around the Martian moon Phobos
… orbits are identified, using the analytical and numerical methodologies of dynamical systems theory. These techniques exploit the improved description of the natural dynamics, enabled by the extended model, to provide low-cost guidance trajectories, that minimize the fuel consumption and extend …
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The Geometry of Isochrons in Planar Systems
… computational methods of that time. We show, via numerical continuation, that the isochrons exhibit extreme sensitivity and feature sharp turns. We observe that the sharp turns and sensitivity of the isochrons are associated with the slow-fast nature of the FitzHugh-Nagumo system; more …
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Adaptive control for enhanced performance of devices and algorithms
… feedback control algorithms in control-based continuation of periodic solutions of a priori unknown dynamical systems under continuous variations in system parameters, independently of their stability. The control-based continuation paradigm applies a numerical continuation algorithm to a …
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On the problem of parallelizing manifold covering algorithms
Continuation methods are numerical algorithms used to determine the solution space of systems of nonlinear equations with associated sets of parameters. Such methods have been very successful in computing solution manifolds of dimension one. For higher dimensional manifolds, different techniques …
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Polynomial continuation in the design of deployable structures
Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of …
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Multidimensional continuation of families of periodic orbits
In this work, we develop an atlas algorithm for continuation of piecewise polynomial discretizations of periodic orbits of ordinary differential equations. Such an algorithm generates a discretized representation of a manifold of such orbits embedded in a larger variable space. Each chart …
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Bifurcations of maps: numerical algorithms and applications
… package {\sc Cl\_MatcontM}. This includes the numerical continuation of fixed points of iterates of the map with one control parameter, detecting and locating their bifurcation points, and their continuation in two control parameters, as well as detection and location of all codim 2 bifurcation …