Using Symbolic Computation to Analyze Zero-Hopf Bifurcations of Polynomial Differential Systems
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Publication:6060388
DOI10.1145/3597066.3597114arXiv2305.11109MaRDI QIDQ6060388
Publication date: 3 November 2023
Published in: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2305.11109
Cites Work
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- Hopf and zero-Hopf bifurcations in the Hindmarsh-Rose system
- Bounding the number of limit cycles for a polynomial Liénard system by using regular chains
- A hybrid symbolic-numerical approach to the center-focus problem
- Zero-Hopf bifurcation in the generalized Michelson system
- On the Hopf-zero bifurcation of the Michelson system
- Hopf bifurcation for some analytic differential systems in \(\mathbb R^3\) via averaging theory
- Normal forms, Melnikov functions and bifurcations of limit cycles
- A complete algorithm for automated discovering of a class of inequality-type theorems
- Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity
- Algebraic approaches to stability analysis of biological systems
- Estimating the number of limit cycles in polynomial systems
- Hopf bifurcation in higher dimensional differential systems via the averaging method
- \(3\)-dimensional Hopf bifurcation via averaging theory of second order
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Elimination methods
- Partial cylindrical algebraic decomposition for quantifier elimination
- Mechanical manipulation for a class of differential systems
- Newton polytopes and the Bezout theorem
- Symbolic computation of normal forms for semi-simple cases
- Computing closed form solutions of first order ODEs using the Prelle- Singer procedure
- Testing stability by quantifier elimination
- Limit cycles bifurcating from a zero-Hopf singularity in arbitrary dimension
- Efficient incremental algorithms for the sparse resultant and the mixed volume
- Zero-Hopf bifurcation in a 3D jerk system
- Symbolic computation for the qualitative theory of differential equations
- An explicit recursive formula for computing the normal forms associated with semisimple cases
- Special algorithm for stability analysis of multistable biological regulatory systems
- Interfacing with PHCpack
- Zero-Hopf bifurcation in a Chua system
- Solving parametric polynomial systems
- Testing sign conditions on a multivariate polynomial and applications
- Qualitative investigation of a gene model using computer algebra algorithms
- An algorithmic approach to small limit cycles of nonlinear differential systems: the averaging method revisited
- AN APPLICATION OF REGULAR CHAIN THEORY TO THE STUDY OF LIMIT CYCLES
- Bifurcation to Quasi-Periodic Tori in the Interaction of Steady State and Hopf Bifurcations
- The Center and Cyclicity Problems
- Using Algebraic Geometry
- Zero-Hopf Periodic Orbits for a Rössler Differential System
- The zero-Hopf bifurcations of a four-dimensional hyperchaotic system
- An Equivalent Formulation of the Averaged Functions via Bell Polynomials
- Analysis of Zero-Hopf Bifurcation in Two Rössler Systems Using Normal Form Theory
- Stability analysis of biological systems with real solution classification
- Higher order averaging theory for finding periodic solutions via Brouwer degree
- Averaging methods in nonlinear dynamical systems
- Elements of applied bifurcation theory