AN APPLICATION OF REGULAR CHAIN THEORY TO THE STUDY OF LIMIT CYCLES
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Publication:2866055
DOI10.1142/S021812741350154XzbMath1277.34033OpenAlexW1978933280MaRDI QIDQ2866055
Pei Yu, Changbo Chen, Robert M. Corless, Yiming Zhang, Marc Moreno Maza
Publication date: 13 December 2013
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s021812741350154x
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theoretical approximation of solutions to ordinary differential equations (34A45) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)
Related Items (22)
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Uses Software
Cites Work
- The \texttt{modpn} library: bringing fast polynomial arithmetic into \texttt{Maple}
- New results on the study of \(Z_q\)-equivariant planar polynomial vector fields
- Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers
- Bit-size estimates for triangular sets in positive dimension
- Symbolic computation of limit cycles associated with Hilbert's 16th problem
- Computation of focus values with applications
- A cubic system with thirteen limit cycles
- Modular algorithms for computing Gröbner bases.
- On some super fault-tolerant Hamiltonian graphs
- Analysis on double Hopf bifurcation using computer algebra with the aid of multiple scales
- Complexity results for triangular sets
- A cubic system with twelve small amplitude limit cycles
- Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
- Real solution isolation using interval arithmetic
- COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
- SYMBOLIC COMPUTATION OF NORMAL FORMS FOR RESONANT DOUBLE HOPF BIFURCATIONS USING A PERTURBATION TECHNIQUE
- Size of coefficients of lexicographical Groöbner bases
- EXISTENCE CONDITIONS OF THIRTEEN LIMIT CYCLES IN A CUBIC SYSTEM
- Comprehensive Triangular Decomposition
- HILBERT'S 16TH PROBLEM FOR QUADRATIC SYSTEMS: NEW METHODS BASED ON A TRANSFORMATION TO THE LIENARD EQUATION
- On improving approximate results of Buchberger's algorithm by Newton's method
- A Cubic System with Eight Small-Amplitude Limit Cycles
- HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
- On hereditarily indecomposable Banach spaces
- A Gröbner free alternative for polynomial system solving
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