Journal of Differential Equations, ISSN 0022-0396, 01/2016, Volume 260, Issue 2, pp. 1690 - 1716

For the cubic–linear polynomial planar differential systems with a finite singular point, we classify the ones which have a local analytic first integral...

Analytic integrability | Cubic–linear planar polynomial differential systems | Secondary | Cubic-linear planar polynomial differential systems | Primary | MATHEMATICS

Analytic integrability | Cubic–linear planar polynomial differential systems | Secondary | Cubic-linear planar polynomial differential systems | Primary | MATHEMATICS

Journal Article

Dynamical Systems, ISSN 1468-9367, 01/2019, Volume 34, Issue 1, pp. 1 - 13

The quartic-linear polynomial differential systems having at least one finite singularity are affine equivalent to systems of the form [Formula omitted.] where...

global C | Planar polynomial differential systems | resonance | canonical region | first integrals | quartic–linear systems | Linear systems | Polynomials | Integrals | Smoothness

global C | Planar polynomial differential systems | resonance | canonical region | first integrals | quartic–linear systems | Linear systems | Polynomials | Integrals | Smoothness

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 09/2017, Volume 263, Issue 6, pp. 3327 - 3369

We consider polynomial vector fields X with a linear type and with homogenous nonlinearities. It is well-known that X has a center at the origin if and only if...

Isochronous center | Holomorphic isochronous center | Uniform isochronous center | Center-foci problem | Darboux's first integral | Weak condition for a center | MATHEMATICS

Isochronous center | Holomorphic isochronous center | Uniform isochronous center | Center-foci problem | Darboux's first integral | Weak condition for a center | MATHEMATICS

Journal Article

International Journal of Bifurcation and Chaos, ISSN 0218-1274, 09/2015, Volume 25, Issue 10, p. 1550131

In this paper, we investigate the number of limit cycles for a class of discontinuous planar differential systems with multiple sectors separated by many rays...

Discontinuous planar system | number of limit cycles | Liénard polynomial system | averaging theory | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Lienard polynomial system | BIFURCATIONS | MULTIDISCIPLINARY SCIENCES | Origins | Amplitudes | Upper bounds | Chaos theory | Bifurcations | Polynomials | Criteria

Discontinuous planar system | number of limit cycles | Liénard polynomial system | averaging theory | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Lienard polynomial system | BIFURCATIONS | MULTIDISCIPLINARY SCIENCES | Origins | Amplitudes | Upper bounds | Chaos theory | Bifurcations | Polynomials | Criteria

Journal Article

Journal of Dynamics and Differential Equations, ISSN 1040-7294, 9/2018, Volume 30, Issue 3, pp. 1295 - 1310

For planar polynomial vector fields of the form $$\begin{aligned} (-y+X(x,y))\dfrac{\partial }{\partial x}+(x+Y(x,y))\dfrac{\partial }{\partial y},...

Ordinary Differential Equations | Uniform isochronous centers | Center-focus problem | Polynomial planar differential system | Mathematics | Applications of Mathematics | Partial Differential Equations | 34C07 | MATHEMATICS | MATHEMATICS, APPLIED | CURVES | 34C Qualitative theory | Equacions diferencials ordinàries | Differential equations | 34 Ordinary differential equations | Matemàtiques i estadística | Classificació AMS | Àrees temàtiques de la UPC | Equacions diferencials i integrals

Ordinary Differential Equations | Uniform isochronous centers | Center-focus problem | Polynomial planar differential system | Mathematics | Applications of Mathematics | Partial Differential Equations | 34C07 | MATHEMATICS | MATHEMATICS, APPLIED | CURVES | 34C Qualitative theory | Equacions diferencials ordinàries | Differential equations | 34 Ordinary differential equations | Matemàtiques i estadística | Classificació AMS | Àrees temàtiques de la UPC | Equacions diferencials i integrals

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 11/2012, Volume 25, Issue 11, pp. 1862 - 1865

The integrability problem consists in finding the class of functions, a first integral of a given planar polynomial differential system must belong to. We...

Darboux theory of integrability | Planar integrability | Polynomial differential systems | MATHEMATICS, APPLIED | 1ST INTEGRALS | NONLINEAR SUPERPOSITION PRINCIPLES | EQUATIONS | VECTOR-FIELDS

Darboux theory of integrability | Planar integrability | Polynomial differential systems | MATHEMATICS, APPLIED | 1ST INTEGRALS | NONLINEAR SUPERPOSITION PRINCIPLES | EQUATIONS | VECTOR-FIELDS

Journal Article

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, ISSN 0035-7596, 2019, Volume 49, Issue 2, pp. 579 - 591

We study the existence of first integrals for the class of reversible and equivariant quadratic polynomial differential systems in the plane. We put special...

MATHEMATICS | Reversible | equivariant | analytic first integral | quadratic planar polynomial equations

MATHEMATICS | Reversible | equivariant | analytic first integral | quadratic planar polynomial equations

Journal Article

Dynamical Systems, ISSN 1468-9367, 01/2019, Volume 34, Issue 1, pp. 1 - 13

The quartic-linear polynomial differential systems having at least one finite singularity are affine equivalent to systems of the form where P and Q are...

Planar polynomial differential systems | global C | 34C05 | 34C23 | 34A34 | quartic-linear systems | resonance | ∞ | first integrals | canonical region

Planar polynomial differential systems | global C | 34C05 | 34C23 | 34A34 | quartic-linear systems | resonance | ∞ | first integrals | canonical region

Journal Article

Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 10/2015, Volume 20, Issue 8, pp. 2657 - 2661

In this paper we find necessary and sufficient conditions in order that the differential systems of the form (x) over dot = x f(y), (y) over dot = g(y), with f...

Analytic first integrals | Planar polynomial systems | Quasi-homogeneous polynomial differential systems | Pseudo-meromorphic first integrals | MATHEMATICS, APPLIED | 1ST INTEGRALS | analytic first integrals | quasi homogeneous polynomial differential systems | pseudo meromorphic first integrals

Analytic first integrals | Planar polynomial systems | Quasi-homogeneous polynomial differential systems | Pseudo-meromorphic first integrals | MATHEMATICS, APPLIED | 1ST INTEGRALS | analytic first integrals | quasi homogeneous polynomial differential systems | pseudo meromorphic first integrals

Journal Article

Qualitative Theory of Dynamical Systems, ISSN 1575-5460, 4/2014, Volume 13, Issue 1, pp. 73 - 87

The cubic–linear polynomial differential systems having at least one finite singularity are affine equivalent to the systems of the form $$\begin{aligned}...

34C05 | 34C25 | Planar differential systems | Global integrability | 34C23 | Normal form | Mathematics | 34C29 | Canonical region | Difference and Functional Equations | Mathematics, general | Resonance | Dynamical Systems and Ergodic Theory | Computer science

34C05 | 34C25 | Planar differential systems | Global integrability | 34C23 | Normal form | Mathematics | 34C29 | Canonical region | Difference and Functional Equations | Mathematics, general | Resonance | Dynamical Systems and Ergodic Theory | Computer science

Journal Article

Acta Applicandae Mathematicae, ISSN 0167-8019, 10/2015, Volume 139, Issue 1, pp. 167 - 186

We introduce several techniques which allow to simplify the expression of the cofactor of Darboux polynomials of polynomial differential systems in $\mathbb...

34C05 | 34C14 | Theoretical, Mathematical and Computational Physics | 34A34 | Planar polynomial differential system | Mathematics | Statistical Physics, Dynamical Systems and Complexity | Cofactor | Birational map | Darboux polynomial | Non-algebraic limit cycle | Mechanics | Mathematics, general | Computer Science, general | INVARIANT ALGEBRAIC-SURFACES | MATHEMATICS, APPLIED | INTEGRABILITY | CURVES | WAVE | SYSTEMS | LIMIT-CYCLES | EQUATION | CHAOTIC ATTRACTOR | Studies | Polynomials | Mathematical analysis | System theory | Differential equations | Algebra | Planes | Computation | Proving | Texts

34C05 | 34C14 | Theoretical, Mathematical and Computational Physics | 34A34 | Planar polynomial differential system | Mathematics | Statistical Physics, Dynamical Systems and Complexity | Cofactor | Birational map | Darboux polynomial | Non-algebraic limit cycle | Mechanics | Mathematics, general | Computer Science, general | INVARIANT ALGEBRAIC-SURFACES | MATHEMATICS, APPLIED | INTEGRABILITY | CURVES | WAVE | SYSTEMS | LIMIT-CYCLES | EQUATION | CHAOTIC ATTRACTOR | Studies | Polynomials | Mathematical analysis | System theory | Differential equations | Algebra | Planes | Computation | Proving | Texts

Journal Article

Studia Universitatis Babes-Bolyai Mathematica, 2016, Volume 61, Issue 1, pp. 77 - 85

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2017, Volume 449, Issue 1, pp. 572 - 579

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...

Piecewise smooth vector fields | Cyclicity | Limit cycle | Averaging theory | EXISTENCE | MATHEMATICS, APPLIED | NUMBER | LINEAR SYSTEMS | DIFFERENTIAL-SYSTEMS | MATHEMATICS | PLANAR FILIPPOV SYSTEMS | 2 ZONES | DYNAMICS | BIFURCATION

Piecewise smooth vector fields | Cyclicity | Limit cycle | Averaging theory | EXISTENCE | MATHEMATICS, APPLIED | NUMBER | LINEAR SYSTEMS | DIFFERENTIAL-SYSTEMS | MATHEMATICS | PLANAR FILIPPOV SYSTEMS | 2 ZONES | DYNAMICS | BIFURCATION

Journal Article

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, ISSN 1575-5460, 04/2014, Volume 13, Issue 1, pp. 73 - 87

The cubic-linear polynomial differential systems having at least one finite singularity are affine equivalent to the systems of the form x' = P(x, y) = bx + cy...

MATHEMATICS | MATHEMATICS, APPLIED | Canonical region | Planar differential systems | Global integrability | 1ST INTEGRALS | Normal form | Resonance | DARBOUX INTEGRABILITY

MATHEMATICS | MATHEMATICS, APPLIED | Canonical region | Planar differential systems | Global integrability | 1ST INTEGRALS | Normal form | Resonance | DARBOUX INTEGRABILITY

Journal Article

International Journal of Pure and Applied Mathematics, ISSN 1311-8080, 2015, Volume 103, Issue 2, pp. 235 - 241

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2012, Volume 394, Issue 1, pp. 416 - 424

We deal with complex planar differential systems having a Darboux first integral H. We present a definition of remarkable values and remarkable curves...

Planar polynomial differential system | Remarkable value | Inverse integrating factor | Darboux first integral | Characteristic polynomial | MATHEMATICS | MATHEMATICS, APPLIED | 1ST INTEGRALS | POLYNOMIAL VECTOR-FIELDS | EQUATIONS | INVARIANT ALGEBRAIC-CURVES | LIMIT-CYCLES

Planar polynomial differential system | Remarkable value | Inverse integrating factor | Darboux first integral | Characteristic polynomial | MATHEMATICS | MATHEMATICS, APPLIED | 1ST INTEGRALS | POLYNOMIAL VECTOR-FIELDS | EQUATIONS | INVARIANT ALGEBRAIC-CURVES | LIMIT-CYCLES

Journal Article

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, ISSN 1531-3492, 12/2019, Volume 24, Issue 12, pp. 6495 - 6509

In this paper we investigate the center problem for the discontinuous piecewise smooth quasi-homogeneous but non-homogeneous polynomial differential systems....

MATHEMATICS, APPLIED | piecewise smooth systems | dynamics | Global center | BIFURCATIONS | GLOBAL DYNAMICS | LIMIT-CYCLES | PLANAR | quasi-homogeneous polynomial systems

MATHEMATICS, APPLIED | piecewise smooth systems | dynamics | Global center | BIFURCATIONS | GLOBAL DYNAMICS | LIMIT-CYCLES | PLANAR | quasi-homogeneous polynomial systems

Journal Article

18.
Full Text
On the Bifurcation of Limit Cycles Due to Polynomial Perturbations of Hamiltonian Centers

Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2017, Volume 14, Issue 2, pp. 1 - 10

We study the number of limit cycles bifurcating from the period annulus of a real planar polynomial Hamiltonian ordinary differential system with a center at...

Ordinary differential system | Primary 34C05 | polynomial system | limit cycle | Melnikov function | planar system | center | Secondary 37C10 | Mathematics, general | Hamiltonian system | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED

Ordinary differential system | Primary 34C05 | polynomial system | limit cycle | Melnikov function | planar system | center | Secondary 37C10 | Mathematics, general | Hamiltonian system | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 360, Issue 1, pp. 168 - 189

We study the uniqueness of limit cycles (periodic solutions that are isolated in the set of periodic solutions) in the scalar ODE x ′ = ∑ k = 1 m a k sin i k (...

Limit cycle | Scalar differential equation | Rigid planar vector field | EXISTENCE | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | NUMBER | ABEL

Limit cycle | Scalar differential equation | Rigid planar vector field | EXISTENCE | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | NUMBER | ABEL

Journal Article

20.
Limit cycle bifurcations of a general Liénard system with polynomial restoring and damping functions

International Journal of Dynamical Systems and Differential Equations, ISSN 1752-3583, 10/2012, Volume 4, Issue 3, pp. 242 - 254

Applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit...

Bifurcation | Limit cycle | Planar polynomial dynamical system | Liénard system | Singular point | Field rotation parameter | Damping | Spirals | Dynamics | Exteriors | Differential equations | Bifurcations | Renovating | Dynamical systems

Bifurcation | Limit cycle | Planar polynomial dynamical system | Liénard system | Singular point | Field rotation parameter | Damping | Spirals | Dynamics | Exteriors | Differential equations | Bifurcations | Renovating | Dynamical systems

Journal Article

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