Veronika Hajnová: New Applications
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en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 21 Jun 2021 13:18:54 GMTMon, 21 Jun 2021 13:18:54 GMTNew applications published by Veronika Hajnováhttps://www.maplesoft.com/images/Application_center_hp.jpgVeronika Hajnová: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=653855
n-fold bifurcation on Mandelbrot set and complex logistic equation fractal
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Analytic derivation of a basin of attractions for fixed point and cycles for Mandelbrot set and the complex logistic equation<img src="https://www.maplesoft.com/view.aspx?si=154661/3fold.png" alt="n-fold bifurcation on Mandelbrot set and complex logistic equation fractal" style="max-width: 25%;" align="left"/>Analytic derivation of a basin of attractions for fixed point and cycles for Mandelbrot set and the complex logistic equationhttps://www.maplesoft.com/applications/view.aspx?SID=154661&ref=FeedMon, 14 Dec 2020 05:00:00 ZLenka PřibylováLenka PřibylováTransformations of phase portraits for linear systems
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Animations of different transformations of vector fields for linear systems of differential equations<img src="https://www.maplesoft.com/view.aspx?si=154663/Phase_portraits_-_linear_systems.png" alt="Transformations of phase portraits for linear systems" style="max-width: 25%;" align="left"/>Animations of different transformations of vector fields for linear systems of differential equationshttps://www.maplesoft.com/applications/view.aspx?SID=154663&ref=FeedFri, 11 Dec 2020 05:00:00 ZLenka PřibylováLenka PřibylováNormal form for the Poincaré-Andronov-Hopf Bifurcation and the Neimark-Sacker Torus Bifurcation
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This sheet implements a method to find a normal form of a dynamical system. The essential background can be found in chapter 19 in Stephen Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos.<img src="https://www.maplesoft.com/view.aspx?si=154662/normal_forms.png" alt="Normal form for the Poincaré-Andronov-Hopf Bifurcation and the Neimark-Sacker Torus Bifurcation" style="max-width: 25%;" align="left"/>This sheet implements a method to find a normal form of a dynamical system. The essential background can be found in chapter 19 in Stephen Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos.https://www.maplesoft.com/applications/view.aspx?SID=154662&ref=FeedFri, 11 Dec 2020 05:00:00 ZLenka PřibylováLenka PřibylováJulia Set
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Generates Julia sets from the unit circle using transformations in the complex plane.<img src="https://www.maplesoft.com/view.aspx?si=154660/Julia.png" alt="Julia Set" style="max-width: 25%;" align="left"/>Generates Julia sets from the unit circle using transformations in the complex plane.https://www.maplesoft.com/applications/view.aspx?SID=154660&ref=FeedFri, 11 Dec 2020 05:00:00 ZLenka PřibylováLenka PřibylováBlue Sky Catastrophe and FOLD-HOPF Bifuraction in Gavrilov-Shilnikov System
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Animation of trajectories near Blue Sky Catastrophe in Gavrilov-Shilnikov System depending on parameters<img src="https://www.maplesoft.com/view.aspx?si=154659/Bluesky.png" alt="Blue Sky Catastrophe and FOLD-HOPF Bifuraction in Gavrilov-Shilnikov System" style="max-width: 25%;" align="left"/>Animation of trajectories near Blue Sky Catastrophe in Gavrilov-Shilnikov System depending on parametershttps://www.maplesoft.com/applications/view.aspx?SID=154659&ref=FeedFri, 11 Dec 2020 05:00:00 ZLenka PřibylováLenka PřibylováCenter manifolds for three-dimensional systems of differential equations
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This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.<img src="https://www.maplesoft.com/view.aspx?si=154575/center2.png" alt="Center manifolds for three-dimensional systems of differential equations" style="max-width: 25%;" align="left"/>This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.https://www.maplesoft.com/applications/view.aspx?SID=154575&ref=FeedSun, 29 Sep 2019 04:00:00 ZVeronika HajnováVeronika HajnováCenter manifolds for two-dimensional systems of differential equations
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This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.<img src="https://www.maplesoft.com/view.aspx?si=154568/center.png" alt="Center manifolds for two-dimensional systems of differential equations" style="max-width: 25%;" align="left"/>This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.https://www.maplesoft.com/applications/view.aspx?SID=154568&ref=FeedSun, 29 Sep 2019 04:00:00 ZVeronika HajnováVeronika HajnováBialternate matrix products and its application in bifurcation theory
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The central theorems in bifurcation theory are normal form theorems. The structure of all the theorems is the same. It claims, under certain assumptions, an arbitrary system of differential, resp, difference, equations is locally topologically equivalent to the normal form. One type of assumption can be formulated as equalities. For generic one-parameter bifurcations, there is always only one equality assumption. It stands as a condition for eigenvalues of the Jacobi matrix of the system. Those assumptions, so-called test functions, are formulated in section Bifurcation of this sheet. Bialternate product is a matrix product, which allows expressing test functions for Hopf and Neimark-Sacker bifurcations detection and continuation.<img src="https://www.maplesoft.com/view.aspx?si=154567/bif.PNG" alt="Bialternate matrix products and its application in bifurcation theory" style="max-width: 25%;" align="left"/>The central theorems in bifurcation theory are normal form theorems. The structure of all the theorems is the same. It claims, under certain assumptions, an arbitrary system of differential, resp, difference, equations is locally topologically equivalent to the normal form. One type of assumption can be formulated as equalities. For generic one-parameter bifurcations, there is always only one equality assumption. It stands as a condition for eigenvalues of the Jacobi matrix of the system. Those assumptions, so-called test functions, are formulated in section Bifurcation of this sheet. Bialternate product is a matrix product, which allows expressing test functions for Hopf and Neimark-Sacker bifurcations detection and continuation.https://www.maplesoft.com/applications/view.aspx?SID=154567&ref=FeedSat, 28 Sep 2019 04:00:00 ZVeronika HajnováVeronika Hajnová