Symbolic computation for the qualitative theory of differential equations
type: Item
instance of: scholarly article
title: Symbolic computation for the qualitative theory of differential equations
author: Bo Huang
author: Wei Niu
author: Dongming Wang
published in: Acta Mathematica Scientia. Series B. (English Edition)
publication date: 2022-10-12T00:00:00Z
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7600118
zbMATH Keywords: biological systems
zbMATH Keywords: center-focus
zbMATH Keywords: limit cycles
zbMATH Keywords: qualitative analysis
zbMATH Keywords: symbolic computation
describes a project that uses: LINLBF
describes a project that uses: DISCOVERER
describes a project that uses: QEPCAD
MaRDI profile type: Publication
full work available at URL: s10473-022-0617-7
OpenAlex ID: W4304092218
Wikidata QID: Q115384350
cites work: Q3264374
cites work: Q4004269
cites work: Q3785211
cites work: Mechanical manipulation for a class of differential systems
cites work: Q3714165
cites work: On the conditions of Kukles for the existence of a Centre
cites work: On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems
cites work: Computing centre conditions for certain cubic systems
cites work: Invariant algebraic curves and conditions for a centre
cites work: Qualitative theory of the Kukles systems: (I) number of critical points
cites work: Kukles revisited: Advances in computing techniques
cites work: Testing stability by quantifier elimination
cites work: Stability analysis of biological systems with real solution classification
cites work: Special algorithm for stability analysis of multistable biological regulatory systems
cites work: Algorithmic Derivation of Centre Conditions
cites work: The Center and Cyclicity Problems
cites work: An application of regular chain theory to the study of limit cycles
cites work: Bounding the number of limit cycles for a polynomial Liénard system by using regular chains
cites work: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
cites work: Efficient computation of zero-dimensional Gröbner bases by change of ordering
cites work: Sparse FGLM algorithms
cites work: A new efficient algorithm for computing Gröbner bases \((F_4)\)
cites work: Q4660688
cites work: Q2716051
cites work: Q5795628
cites work: On the theories of triangular sets
cites work: Elimination methods
cites work: Using Algebraic Geometry
cites work: Q4079605
cites work: Partial cylindrical algebraic decomposition for quantifier elimination
cites work: A complete algorithm for automated discovering of a class of inequality-type theorems
cites work: Solving parametric polynomial systems
cites work: Q3345088
cites work: Algebraic approaches to stability analysis of biological systems
cites work: Nonlinear control system design by quantifier elimination
cites work: A semi-algebraic approach for asymptotic stability analysis
cites work: Discovering polynomial Lyapunov functions for continuous dynamical systems
cites work: Algebraic analysis of stability and bifurcation of a self-assembling micelle system
cites work: Q3485188
cites work: Computing Hopf Bifurcations I
cites work: Q3485221
cites work: An algorithm for the computation of Hopf bifurcation points in comparison with other methods
cites work: Criterion of Hopf bifurcations without using eigenvalues
cites work: Deciding Hopf bifurcations by quantifier elimination in a software-component architecture
cites work: Limit cycle behavior in three- or higher-dimensional non-linear systems: the Lotka-Volterra example
cites work: Elements of applied bifurcation theory
cites work: Q3948194
cites work: Defining Functions for Multiple Hopf Bifurcations
cites work: Probleme General de la Stabilite du Mouvement. (AM-17)
cites work: Implementation of a new algorithm of computation of the Poincaré-Lyapunov constants.
cites work: Q5474766
cites work: Computation of focus values with applications
cites work: A method of constructing cycles without contact around a weak focus
cites work: On some open problems in planar differential systems and Hilbert's 16th problem
cites work: On a certain generalization of Bautin's theorem

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: The classification of reversible cubic systems with center

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q5832271

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q5844069

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q3049174

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Polynomial systems from certain differential equations

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q3840840

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: An elimination method for polynomial systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q4525303

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Center conditions for generalized polynomial Kukles systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Integrability of a linear center perturbed by a fifth degree homogeneous polynomial

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Centers for the Kukles homogeneous systems with odd degree

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: CENTERS FOR THE KUKLES HOMOGENEOUS SYSTEMS WITH EVEN DEGREE

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Algebraic Particular Integrals, Integrability and the Problem of the Center

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: The center problem on a center manifold in \(\mathbb{R}^{3}\)

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Center problem for third-order ODEs

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: A hybrid symbolic-numerical approach to the center-focus problem

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Varieties of local integrability of analytic differential systems and their applications

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q3602781

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q5832269

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Introduction to analyzable functions and constructive proof of the Dulac conjecture

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q5474767

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q3871220

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: A cubic system with thirteen limit cycles

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q3709504

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Polynomial systems: a lower bound for the Hilbert numbers

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Lower bounds for the Hilbert number of polynomial systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: BIFURCATION OF LIMIT CYCLES IN A FOURTH-ORDER NEAR-HAMILTONIAN SYSTEM

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: On the number of limit cycles of a \(\mathbb{Z}_4\)-equivariant quintic near-Hamiltonian system

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Bifurcations of limit cycles in a \(Z_{4}\)-equivariant quintic planar vector field

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: A class of cubic differential systems with 6-tuple focus

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: A Cubic System with Eight Small-Amplitude Limit Cycles

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: A cubic system with eight small-amplitude limit cycles

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Symbolic computation of limit cycles associated with Hilbert's 16th problem

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Weak centers and bifurcation of critical periods in reversible cubic systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Two limit cycles in three-dimensional Lotka-Volterra systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Differential equations with symbolic computation.

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Semi-algebraic Description of the Equilibria of Dynamical Systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q5496558

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Twelve limit cycles around a singular point in a planar cubic-degree polynomial system

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: The cyclicity of a cubic system with nonradical Bautin ideal

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Estimating the number of limit cycles in polynomial systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Normal forms, Melnikov functions and bifurcations of limit cycles

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Hopf bifurcation in higher dimensional differential systems via the averaging method

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Hopf bifurcation for some analytic differential systems in \(\mathbb R^3\) via averaging theory

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Computation of normal forms via a perturbation technique

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Symbolic computation of normal forms for semi-simple cases

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Analysis of Zero-Hopf Bifurcation in Two Rössler Systems Using Normal Form Theory

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: An explicit recursive formula for computing the normal forms associated with semisimple cases

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: \(3\)-dimensional Hopf bifurcation via averaging theory of second order

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q1233671

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Higher order averaging theory for finding periodic solutions via Brouwer degree

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Averaging methods in nonlinear dynamical systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q4930153

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Limit cycles bifurcating from a zero-Hopf singularity in arbitrary dimension

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Equivalence of the Melnikov function method and the averaging method

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Limit cycles of differential equations

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Strongly nonlinear oscillators. Analytical solutions

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-figure loop

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Bifurcations of limit cycles for a quintic Hamiltonian system with a double cuspidal loop

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: The perturbations of a class of hyper-elliptic Hamilton systems with a double homoclinic loop through a nilpotent saddle

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: A Chebyshev criterion for Abelian integrals

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Bounding the number of zeros of certain abelian integrals

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q5496525

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Bounding the number of limit cycles for parametric Liénard systems using symbolic computation methods

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Bifurcation of Limit Cycles in Small Perturbation of a Class of Liénard Systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q5416050

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Exact bound on the number of zeros of abelian integrals for two hyper-elliptic Hamiltonian systems of degree 4

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q3040961

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Simple mathematical models with very complicated dynamics

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Efficient Methods to Compute Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Identifying the parametric occurrence of multiple steady states for some biological networks

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Multistationarity in structured reaction networks

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: A family of sparse polynomial systems arising in chemical reaction systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q4329395

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: The structure of LaSalle's invariant set for Lotka-Volterra systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Computer aided proof for the global stability of Lotka-Volterra systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Quasi-steady-state laws in reversible model of enzyme kinetics

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Towards an automated reduction method for polynomial ODE models of biochemical reaction systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q4227290

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Model reduction of chemical reaction systems using elimination

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Algebraic stability criteria and symbolic derivation of stability conditions for feedback control systems

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Analysis of Snapback Repellers Using Methods of Symbolic Computation

Symbolic computation for the qualitative theory of differential equations (cites work)
cites work: Q1986483

Symbolic computation for the qualitative theory of differential equations (DOI)
DOI: 10.1007/S10473-022-0617-7