Symbolic computation for the qualitative theory of differential equations
DOI10.1007/s10473-022-0617-7OpenAlexW4304092218WikidataQ115384350 ScholiaQ115384350MaRDI QIDQ2080988
Dongming Wang, Wei Niu, Bo Huang
Publication date: 12 October 2022
Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10473-022-0617-7
Symbolic computation and algebraic computation (68W30) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20)
Related Items (1)
Uses Software
Cites Work
- Model reduction of chemical reaction systems using elimination
- Quasi-steady-state laws in reversible model of enzyme kinetics
- The center problem on a center manifold in \(\mathbb{R}^{3}\)
- Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification
- Bounding the number of limit cycles for a polynomial Liénard system by using regular chains
- Center conditions for generalized polynomial Kukles systems
- Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis
- A hybrid symbolic-numerical approach to the center-focus problem
- Hopf bifurcation for some analytic differential systems in \(\mathbb R^3\) via averaging theory
- Towards an automated reduction method for polynomial ODE models of biochemical reaction systems
- On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle
- Kukles revisited: Advances in computing techniques
- Bounding the number of zeros of certain abelian integrals
- Normal forms, Melnikov functions and bifurcations of limit cycles
- Lower bounds for the Hilbert number of polynomial systems
- Symbolic computation of limit cycles associated with Hilbert's 16th problem
- Varieties of local integrability of analytic differential systems and their applications
- Differential equations with symbolic computation.
- Computation of focus values with applications
- A complete algorithm for automated discovering of a class of inequality-type theorems
- Limit cycles of differential equations
- On the number of limit cycles of a \(\mathbb{Z}_4\)-equivariant quintic near-Hamiltonian system
- A class of cubic differential systems with 6-tuple focus
- Algebraic approaches to stability analysis of biological systems
- Bifurcations of limit cycles in a \(Z_{4}\)-equivariant quintic planar vector field
- Estimating the number of limit cycles in polynomial systems
- Bifurcations of limit cycles for a quintic Hamiltonian system with a double cuspidal loop
- Hopf bifurcation in higher dimensional differential systems via the averaging method
- A cubic system with thirteen limit cycles
- A semi-algebraic approach for asymptotic stability analysis
- \(3\)-dimensional Hopf bifurcation via averaging theory of second order
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- An algorithm for the computation of Hopf bifurcation points in comparison with other methods
- Elimination methods
- A method of constructing cycles without contact around a weak focus
- The structure of LaSalle's invariant set for Lotka-Volterra systems
- Partial cylindrical algebraic decomposition for quantifier elimination
- Mechanical manipulation for a class of differential systems
- Computing centre conditions for certain cubic systems
- 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
- Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
- A new efficient algorithm for computing Gröbner bases \((F_4)\)
- Symbolic computation of normal forms for semi-simple cases
- Efficient computation of zero-dimensional Gröbner bases by change of ordering
- Criterion of Hopf bifurcations without using eigenvalues
- An elimination method for polynomial systems
- A cubic system with eight small-amplitude limit cycles
- The classification of reversible cubic systems with center
- Nonlinear control system design by quantifier elimination
- Testing stability by quantifier elimination
- Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
- Implementation of a new algorithm of computation of the Poincaré-Lyapunov constants.
- Deciding Hopf bifurcations by quantifier elimination in a software-component architecture
- Weak centers and bifurcation of critical periods in reversible cubic systems
- A family of sparse polynomial systems arising in chemical reaction systems
- Two limit cycles in three-dimensional Lotka-Volterra systems
- Sparse FGLM algorithms
- Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points
- Limit cycles bifurcating from a zero-Hopf singularity in arbitrary dimension
- On the theories of triangular sets
- Polynomial systems from certain differential equations
- Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
- Computer aided proof for the global stability of Lotka-Volterra systems
- 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
- Algebraic analysis of stability and bifurcation of a self-assembling micelle system
- Exact bound on the number of zeros of abelian integrals for two hyper-elliptic Hamiltonian systems of degree 4
- Identifying the parametric occurrence of multiple steady states for some biological networks
- An explicit recursive formula for computing the normal forms associated with semisimple cases
- Twelve limit cycles around a singular point in a planar cubic-degree polynomial system
- Special algorithm for stability analysis of multistable biological regulatory systems
- The cyclicity of a cubic system with nonradical Bautin ideal
- Multistationarity in structured reaction networks
- Discovering polynomial Lyapunov functions for continuous dynamical systems
- Solving parametric polynomial systems
- Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems
- On some open problems in planar differential systems and Hilbert's 16th problem
- Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-figure loop
- Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation
- Equivalence of the Melnikov function method and the averaging method
- The perturbations of a class of hyper-elliptic Hamilton systems with a double homoclinic loop through a nilpotent saddle
- Bounding the number of limit cycles for parametric Liénard systems using symbolic computation methods
- CENTER PROBLEM FOR THIRD-ORDER ODEs
- AN APPLICATION OF REGULAR CHAIN THEORY TO THE STUDY OF LIMIT CYCLES
- COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
- LIMIT CYCLE BEHAVIOR IN THREE- OR HIGHER-DIMENSIONAL NON-LINEAR SYSTEMS: THE LOTKA–VOLTERRA EXAMPLE
- On the conditions of Kukles for the existence of a Centre
- A Chebyshev criterion for Abelian integrals
- Semi-algebraic Description of the Equilibria of Dynamical Systems
- Computing Hopf Bifurcations I
- Algebraic Particular Integrals, Integrability and the Problem of the Center
- On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems
- The Center and Cyclicity Problems
- BIFURCATION OF LIMIT CYCLES IN A FOURTH-ORDER NEAR-HAMILTONIAN SYSTEM
- Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits
- Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems
- A Cubic System with Eight Small-Amplitude Limit Cycles
- Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
- Invariant algebraic curves and conditions for a centre
- Defining Functions for Multiple Hopf Bifurcations
- Analysis of Snapback Repellers Using Methods of Symbolic Computation
- HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
- Using Algebraic Geometry
- Polynomial systems: a lower bound for the Hilbert numbers
- On a certain generalization of Bautin's theorem
- Algebraic stability criteria and symbolic derivation of stability conditions for feedback control systems
- CENTERS FOR THE KUKLES HOMOGENEOUS SYSTEMS WITH EVEN DEGREE
- Analysis of Zero-Hopf Bifurcation in Two Rössler Systems Using Normal Form Theory
- Efficient Methods to Compute Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates
- Centers for the Kukles homogeneous systems with odd degree
- Stability analysis of biological systems with real solution classification
- Algorithmic Derivation of Centre Conditions
- HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
- Simple mathematical models with very complicated dynamics
- Bifurcation of Limit Cycles in Small Perturbation of a Class of Liénard Systems
- Higher order averaging theory for finding periodic solutions via Brouwer degree
- Probleme General de la Stabilite du Mouvement. (AM-17)
- Averaging methods in nonlinear dynamical systems
- Elements of applied bifurcation theory
- Strongly nonlinear oscillators. Analytical solutions
- Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles
- Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Symbolic computation for the qualitative theory of differential equations