Results 1 to 10 of about 299,219 (282)
Rigid Polynomial Differential Systems with Homogeneous Nonlinearities
MathematicsPlanar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the pendulum clock of Christiaan Huygens in 1656; since then, the interest for the rigid systems has been
Jaume Llibre
doaj +4 more sources
Anais da Academia Brasileira de Ciências, 2021 Poincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class of Liénard differential equations
JAUME LLIBRE +2 more
doaj +1 more source
Bifurcations of the Riccati Quadratic Polynomial Differential Systems [PDF]
International Journal of Bifurcation and Chaos, 2021 In this paper, we characterize the global phase portrait of the Riccati quadratic polynomial differential system [Formula: see text] with [Formula: see text], [Formula: see text] nonzero (otherwise the system is a Bernoulli differential system), [Formula: see text] (otherwise the system is a Liénard differential system), [Formula: see text] a ...
Jaume Llibre +2 more
openaire +5 more sources
Polynomial Noises for Nonlinear Systems with Nonlinear Impulses and Time-Varying Delays
Mathematics, 2022 It is known that random noises have a significant impact on differential systems. Recently, the influences of random noises for impulsive systems have been started.
Lichao Feng +3 more
doaj +1 more source
Maximum number of limit cycles for generalized Liénard polynomial differential systems [PDF]
Mathematica Bohemica, 2021 We consider limit cycles of a class of polynomial differential systems of the form \begin{cases} \dot{x}=y, \dot{y}=-x-\varepsilon(g_{21}( x) y^{2\alpha+1} +f_{21}(x) y^{2\beta})-\varepsilon^2(g_{22}( x) y^{2\alpha+1}+f_{22}( x) y^{2\beta}), \end ...
Aziza Berbache +2 more
doaj +1 more source
Axioms, 2022 This paper discusses the robust stability and stabilization of polynomial fractional differential (PFD) systems with a Caputo derivative using the sum of squares. In addition, it presents a novel method of stability and stabilization for PFD systems.
Hassan Yaghoubi +2 more
doaj +1 more source
Algebraic limit cycles for quadratic polynomial differential systems [PDF]
Discrete & Continuous Dynamical Systems - B, 2018 AbstractAlgebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and a few years later the following conjecture appeared: quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that a quadratic polynomial differential system having an invariant algebraic curve with at most ...
Llibre, Jaume, Valls, Clàudia
openaire +8 more sources
Dynamics of the polynomial differential systems
Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2023 In general, there are several free parameters. By using a method introduced in a previous paper, we obtain a sequence of algebraic a proximations to the bifurcationsets,in the parameter ...
Feneniche Fatima, Rezaoui Med Salem
openaire +1 more source
New optical soliton solutions to the (n+1) dimensional time fractional order Sinh-Gordon equation
Results in Physics, 2023 This article studies and constructs new optical soliton solutions for the (n+1)-dimensional time fractional order Sinh-Gordon equation. First, we change the differential equation into Ordinary differential equation which is connected with a quartic ...
Da Shi, Zhao Li
doaj +1 more source
Strongly formal Weierstrass non-integrability for polynomial differential systems in $\mathbb{C}^2$
Electronic Journal of Qualitative Theory of Differential Equations, 2020 Recently it has been given a criterion for determining the weakly formal Weierstrass non-integrability of polynomial differential systems in $\mathbb{C}^2$.
Jaume Giné, Jaume Llibre
doaj +1 more source