scholarly journals A general method for the existence of periodic solutions of differential systems in the plane

2012 ◽  
Vol 252 (2) ◽  
pp. 1369-1391 ◽  
Author(s):  
Alessandro Fonda ◽  
Andrea Sfecci
Keyword(s):  
Periodic Solutions ◽  
Differential Systems ◽  
Existence Of Periodic Solutions ◽  
General Method

scholarly journals Existence for Singular Periodic Problems: A Survey of Recent Results

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Jifeng Chu ◽  
Juntao Sun ◽  
Patricia J. Y. Wong
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Impulsive Differential Equations ◽  
Differential Systems ◽  
Singular Differential Equations ◽  
Periodic Problems ◽  
Existence Of Periodic Solutions

We present a survey on the existence of periodic solutions of singular differential equations. In particular, we pay our attention to singular scalar differential equations, singular damped differential equations, singular impulsive differential equations, and singular differential systems.

scholarly journals Periodic Solutions of a Periodic FitzHugh–Nagumo System

2015 ◽  
Vol 25 (13) ◽  
pp. 1550180 ◽  
Author(s):  
Jaume Llibre ◽  
Claudio Vidal
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Existence Of Periodic Solutions

Recently some interest has appeared for the periodic FitzHugh–Nagumo differential systems. Here, we provide sufficient conditions for the existence of periodic solutions in such differential systems.

scholarly journals ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF NONLINEAR DIFFERENTIAL SYSTEMS

1993 ◽  
Vol 24 (2) ◽  
pp. 173-188
Author(s):  
LIHONG HUANG ◽  
JIANSHE YU
Keyword(s):  
Periodic Solutions ◽  
Special Form ◽  
Differential Systems ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions ◽  
Nonlinear Differential Systems

In this paper three theorems on the existence of nontrivial periodic solutions of the system \[ dx/dt =e(y)\]\[dy/dt =-e(y)f(x)- g(x)\] are proved, which not only generalize some known results on the existence of periodic solutions of Lienard's system (i.e. the special form for $e(y) = y$), but also relax or eliminate some traditional assumptions.

scholarly journals On the Generalized Reflective Function of the Three-Degree Polynomial Differential System

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Reflective Function ◽  
Degree Polynomial ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Polynomial Differential System ◽  
Existence Of Periodic Solutions

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.

scholarly journals Periodic Solutions Generated by Impulses for State-Dependent Impulsive Differential Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Qizhen Xiao ◽  
Binxiang Dai
Keyword(s):  
Differential Equation ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Impulsive Differential Equation ◽  
Geometrical Analysis ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Analysis Methods ◽  
State Dependent ◽  
Existence Of Periodic Solutions

We study the existence of periodic solutions for a class of state-dependent impulsive differential systems via geometrical analysis methods. Our results show that these periodic solutions are generated by impulses. Moreover, numerical simulations are used to examine the existence of the periodic solutions.

scholarly journals Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Amar Makhlouf ◽  
Lilia Bousbiat
Keyword(s):  
Small Parameter ◽  
Real Number ◽  
Periodic Solutions ◽  
Differential System ◽  
Sufficient Conditions ◽  
Periodic Functions ◽  
Third Order ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Existence Of Periodic Solutions

We provide sufficient conditions for the existence of periodic solutions of the polynomial third order differential systemx.=-y+εP(x,y,z)+h1(t),  y.=x+εQ(x,y,z)+h2(t),  and  z.=az+εR(x,y,z)+h3(t), whereP,Q, andRare polynomials in the variablesx,y, andzof degreen,  hi(t)=hi(t+2π)withi=1,2,3being periodic functions,ais a real number, andεis a small parameter.

scholarly journals Periodic solutions for differential systems in ℝ3 and ℝ4

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Amina Feddaoui ◽  
Jaume Llibre ◽  
Chemseddine Berhail ◽  
Amar Makhlouf
Keyword(s):  
Small Parameter ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Periodic Functions ◽  
Differential Systems ◽  
Existence Of Periodic Solutions

AbstractWe provide sufficient conditions for the existence of periodic solutions for the differential systems \matrix{{x' = y,\;\;\;y' = z,\;\;\;z' = - y - \varepsilon F(t,x,y,z),\;\;\;{\rm{and}}} \cr {x' = y,\quad y' = - x - \varepsilon G(t,x,y,z,u),\quad z' = u,\quad u' = - z - \varepsilon H(t,x,y,z,u),} \hfill \cr } where F, G and H are 2π–periodic functions in the variable t and ɛ is a small parameter. These differential systems appear frequently in many problems coming from the sciences and the engineering.

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