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Local cyclicity in low degree planar piecewise polynomial vector fields
(Elsevier B.V., 2021-08-01)
In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small ...
STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS
(Texas State Univ, 2012-09-22)
Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise ...
Combinatorial classification of piecewise hereditary algebras
(De Gruyter, 2011-01)
We use the characteristic polynomial of the Coxeter matrix of an algebra to complete the combinatorial classification of piecewise hereditary algebras which Happel gave in terms of the trace of the Coxeter matrix. We also ...
Algorithms for network piecewise-linear programs: A comparative study
(1997-02-16)
Piecewise-Linear Programming (PLP) is an important area of Mathematical Programming and concerns the minimisation of a convex separable piecewise-linear objective function, subject to linear constraints. In this paper a ...
Limit cycles of discontinuous piecewise polynomial vector fields
(2017-05-01)
When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we ...
Stable piecewise polynomial vector fields
(2012-09-22)
Let N = {y > 0} and S = {y < 0} be the semi-planes of ℝ 2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise ...
STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS
(TEXAS STATE UNIVSAN MARCOS, 2012)
Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise ...
Limit cycles via higher order perturbations for some piecewise differential systems
(Elsevier B.V., 2018-05-15)
A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x', y') = (-y + epsilon f(x, y, epsilon), x + epsilon g(x, y, epsilon)). In this paper we study the limit cycles that bifurcate ...
Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness
(2021-01-01)
Dynamical systems subject to intermittent contact are often modeled with piecewise-smooth contact forces. However, the discontinuous nature of the contact can cause inaccuracies in numerical results or failure in numerical ...
Limit Cycles For M-piecewise Discontinuous Polynomial Li,nard Differential Equations
(SPRINGER BASEL AGBASEL, 2015)