Symbolic computation for the qualitative theory of differential equations (Q2080988)

scientific article; zbMATH DE number 7600118

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English	Symbolic computation for the qualitative theory of differential equations	scientific article; zbMATH DE number 7600118

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instance of

scholarly article

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title

Symbolic computation for the qualitative theory of differential equations (English)

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Acta Mathematica Scientia. Series B. (English Edition)

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publication date

12 October 2022

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zbMATH Keywords

biological systems

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center-focus

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limit cycles

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qualitative analysis

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symbolic computation

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describes a project that uses

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full work available at URL

https://doi.org/10.1007/s10473-022-0617-7

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Mechanical manipulation for a class of differential systems

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Q3714165

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On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems

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Computing centre conditions for certain cubic systems

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Invariant algebraic curves and conditions for a centre

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Qualitative theory of the Kukles systems: (I) number of critical points

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Kukles revisited: Advances in computing techniques

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Testing stability by quantifier elimination

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Stability analysis of biological systems with real solution classification

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Special algorithm for stability analysis of multistable biological regulatory systems

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Algorithmic Derivation of Centre Conditions

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The Center and Cyclicity Problems

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An application of regular chain theory to the study of limit cycles

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Sparse FGLM algorithms

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Q4660688

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Q2716051

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Q5795628

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Elimination methods

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Using Algebraic Geometry

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Q4079605

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Solving parametric polynomial systems

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Q3345088

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Algebraic approaches to stability analysis of biological systems

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Nonlinear control system design by quantifier elimination

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A semi-algebraic approach for asymptotic stability analysis

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Q3485221

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An algorithm for the computation of Hopf bifurcation points in comparison with other methods

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Criterion of Hopf bifurcations without using eigenvalues

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Elements of applied bifurcation theory

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Q3948194

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Defining Functions for Multiple Hopf Bifurcations

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Probleme General de la Stabilite du Mouvement. (AM-17)

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Implementation of a new algorithm of computation of the Poincaré-Lyapunov constants.

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Q5474766

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Computation of focus values with applications

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A method of constructing cycles without contact around a weak focus

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On a certain generalization of Bautin's theorem

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The classification of reversible cubic systems with center

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Q5832271

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Q5844069

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Q3049174

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Polynomial systems from certain differential equations

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Q3840840

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An elimination method for polynomial systems

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Q4525303

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Center conditions for generalized polynomial Kukles systems

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Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

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Integrability of a linear center perturbed by a fifth degree homogeneous polynomial

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Centers for the Kukles homogeneous systems with odd degree

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CENTERS FOR THE KUKLES HOMOGENEOUS SYSTEMS WITH EVEN DEGREE

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Algebraic Particular Integrals, Integrability and the Problem of the Center

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The center problem on a center manifold in \(\mathbb{R}^{3}\)

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Center problem for third-order ODEs

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A hybrid symbolic-numerical approach to the center-focus problem

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Varieties of local integrability of analytic differential systems and their applications

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Q5832269

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Introduction to analyzable functions and constructive proof of the Dulac conjecture

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A cubic system with thirteen limit cycles

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Lower bounds for the Hilbert number of polynomial systems

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BIFURCATION OF LIMIT CYCLES IN A FOURTH-ORDER NEAR-HAMILTONIAN SYSTEM

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Bifurcations of limit cycles in a \(Z_{4}\)-equivariant quintic planar vector field

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Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation

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HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

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A class of cubic differential systems with 6-tuple focus

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A Cubic System with Eight Small-Amplitude Limit Cycles

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A cubic system with eight small-amplitude limit cycles

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Symbolic computation of limit cycles associated with Hilbert's 16th problem

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Weak centers and bifurcation of critical periods in reversible cubic systems

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Two limit cycles in three-dimensional Lotka-Volterra systems

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Differential equations with symbolic computation.

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Twelve limit cycles around a singular point in a planar cubic-degree polynomial system

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The cyclicity of a cubic system with nonradical Bautin ideal

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Normal forms, Melnikov functions and bifurcations of limit cycles

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HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS

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Hopf bifurcation in higher dimensional differential systems via the averaging method

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Hopf bifurcation for some analytic differential systems in \(\mathbb R^3\) via averaging theory

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Computation of normal forms via a perturbation technique

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\(3\)-dimensional Hopf bifurcation via averaging theory of second order

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The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale

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Higher order averaging theory for finding periodic solutions via Brouwer degree

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Averaging methods in nonlinear dynamical systems

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Q4930153

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Limit cycles bifurcating from a zero-Hopf singularity in arbitrary dimension

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Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems

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Nonlinear oscillations, dynamical systems, and bifurcations of vector fields

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Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor

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Equivalence of the Melnikov function method and the averaging method

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Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields

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Limit cycles of differential equations

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Strongly nonlinear oscillators. Analytical solutions

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Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles

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Algebraic and symbolic computation methods in dynamical systems. Based on articles written for the invited sessions of the 5th symposium on system structure and control, IFAC, Grenoble, France, February 4--6, 2013 and of the 21st international symposium on mathematical theory of networks and systems (MTNS 2014), Groningen, the Netherlands, July 7--11, 2014

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Identifiers

Mathematics Subject Classification ID

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10.1007/S10473-022-0617-7

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Sitelinks

Mathematics(1 entry)

mardi Publication:2080988