Related papers: Using Symbolic Computation to Analyze Zero-Hopf Bi…
In this paper, we study the bifurcation of limit cycles in Lienard systems of the form dot(x)=y-F(x), dot(y)=-x, where F(x) is an odd polynomial that contains, in general, several free parameters. By using a method introduced in a previous…
In this work we present and study an iterative algorithm used to asymptotically solve nonlinear differential equations. This algorithm (Iterative First Order HAM or IFOHAM) is based on the first order equation of the Homotopy Analysis…
This work introduces a parametric simulation-free reduced order model for incompressible flows undergoing a Hopf bifurcation, leveraging the parametrisation method for invariant manifolds. Unlike data-driven approaches, this method operates…
By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…
In this paper, we present a geometric approach to exponentially small splitting in zero-Hopf bifurcations of arbitrary co-dimension. In further details, we consider a family of problems that generalizes the third order…
Dynamic models describe phenomena across scientific disciplines, yet to make these models useful in application the unknown parameter values of the models must be determined. Discrete-time dynamic models are widely used to model biological…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
Using $p$-adic numbers, we partially categorize the cycles of a sizable class of polynomial dynamical systems. In turn, we prove a few results related to the non-trivial cycles of the $\textit{Collatz map}$ $\text{Col} : \mathbb{Z}_+ \to…
Algorithms are described and Maple implementations are provided for finding all quandles of order $n$, as well as computing all homomorphisms between two finite quandles or from a finitely presented quandle (e.g., a knot quandle) to a…
In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…
We consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials…
Counting the number of perfect matchings in bipartite graphs, or equivalently computing the permanent of 0-1 matrices, is an important combinatorial problem that has been extensively studied by theoreticians and practitioners alike. The…
A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…
Connected branches of periodic orbits originating at a Hopf bifurcation point of a differential system are considered. A computable estimate for the range of amplitudes of periodic orbits contained in the branch is provided under the…
An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary…
Dynamical properties of ultradiscrete Hopf bifurcation, similar to those of the standard Hopf bifurcation, are discussed by proposing a simple model of ultradiscrete equations with max-plus algebra. In ultradiscrete Hopf bifurcation, limit…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
In this work we study the periodic orbits which bifurcate from a zero-Hopf bifurcations that a Lorenz-Haken system in R 4 can exhibit. The main tool used is the averaging theory.
We focus on a chaotic differential system in 3-dimension, including an absolute term and a line of equilibrium points. Which describes in the following This system has an implementation in electronic components. The first purpose of this…
We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in…