polynomial differential system
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2021 ◽  
Vol 31 (06) ◽  
pp. 2150094
Author(s):  
Jaume Llibre ◽  
Bruno D. Lopes ◽  
Paulo R. da Silva

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 polynomial of degree at most [Formula: see text], [Formula: see text] and [Formula: see text] polynomials of degree at most 2, and the maximum of the degrees of [Formula: see text] and [Formula: see text] is 2. We give the complete description of the phase portraits in the Poincaré disk (i.e. in the compactification of [Formula: see text] adding the circle [Formula: see text] of the infinity) modulo topological equivalence.


2020 ◽  
Vol 53 (2) ◽  
pp. 3266-3271
Author(s):  
Matteo Tacchi ◽  
Carmen Cardozo ◽  
Didier Henrion ◽  
Jean Bernard Lasserre

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Jian Zhou ◽  
Shiyin Zhao

The structure of the generalized reflective function of three-degree polynomial differential systems is considered in this paper. The generated results are used for discussing the existence of periodic solutions of these systems.


2019 ◽  
Vol 29 (05) ◽  
pp. 1950069 ◽  
Author(s):  
Jaume Giné ◽  
Claudia Valls

In this paper, we characterize all the Liouvillian first integrals of a cubic polynomial differential system that contains the van der Pol and the Duffing oscillators. It is also shown that the centers correspond to the Liouville integrable cases.


2018 ◽  
Vol 28 (05) ◽  
pp. 1850058 ◽  
Author(s):  
Murilo R. Cândido ◽  
Jaume Llibre

In this paper, we study the periodic solutions bifurcating from a nonisolated zero–Hopf equilibrium in a polynomial differential system of degree two in [Formula: see text]. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero–Hopf equilibrium. This new result is applied for studying the periodic solutions of differential systems in [Formula: see text] having [Formula: see text]-scroll chaotic attractors.


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