scholarly journals Poincaré Map and Periodic Solutions of First-Order Impulsive Differential Equations on Moebius Stripe

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Yefeng He ◽  
Yepeng Xing
Keyword(s):  
Periodic Orbit ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Poincaré Map ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Poincare Map ◽  
First Order ◽  
Existence And Stability ◽  
Stability And Bifurcations

This paper is mainly concerned with the existence, stability, and bifurcations of periodic solutions of a certain scalar impulsive differential equations on Moebius stripe. Some sufficient conditions are obtained to ensure the existence and stability of one-side periodic orbit and two-side periodic orbit of impulsive differential equations on Moebius stripe by employing displacement functions. Furthermore, double-periodic bifurcation is also studied by using Poincaré map.

scholarly journals Variational Approach to Impulsive Differential Equations with Singular Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Naima Daoudi-Merzagui ◽  
Abdelkader Boucherif
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Periodic Solutions ◽  
Variational Approach ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Singular Nonlinearities ◽  
Existence Of Periodic Solutions

We discuss the existence of periodic solutions for nonautonomous second order differential equations with singular nonlinearities. Simple sufficient conditions that enable us to obtain many distinct periodic solutions are provided. Our approach is based on a variational method.

scholarly journals A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 677 ◽  
Author(s):  
Kadry ◽  
Alferov ◽  
Ivanov ◽  
Korolev ◽  
Selitskaya
Keyword(s):  
Functional Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Lower Bounds ◽  
New Method ◽  
Upper And Lower Bounds ◽  
First Order ◽  
Periodic Problems ◽  
Existence And Stability

In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.

scholarly journals The Dynamics of a Predator-Prey System with State-Dependent Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hunki Baek
Keyword(s):  
Feedback Control ◽  
Periodic Solutions ◽  
Poincaré Map ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
Poincare Map ◽  
Predator Prey ◽  
Prey System ◽  
State Dependent ◽  
Fold Bifurcation

A Lotka-Volterra-type predator-prey system with state-dependent feedback control is investigated in both theoretical and numerical ways. Using the Poincaré map and the analogue of the Poincaré criterion, the sufficient conditions for the existence and stability of semitrivial periodic solutions and positive periodic solutions are obtained. In addition, we show that there is no positive periodic solution with period greater than and equal to three under some conditions. The qualitative analysis shows that the positive period-one solution bifurcates from the semitrivial solution through a fold bifurcation. Numerical simulations to substantiate our theoretical results are provided. Also, the bifurcation diagrams of solutions are illustrated by using the Poincaré map, and it is shown that the chaotic solutions take place via a cascade of period-doubling bifurcations.

scholarly journals Existence of solutions for first-order Hamiltonian random impulsive differential equations with Dirichlet boundary conditions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yu Guo ◽  
Xiao-Bao Shu ◽  
Qianbao Yin
Keyword(s):  
Differential Equations ◽  
Critical Point ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Energy Functional ◽  
Dirichlet Boundary Conditions ◽  
Mountain Pass Lemma ◽  
First Order

<p style='text-indent:20px;'>In this paper, we study the sufficient conditions for the existence of solutions of first-order Hamiltonian random impulsive differential equations under Dirichlet boundary value conditions. By using the variational method, we first obtain the corresponding energy functional. And by using Legendre transformation, we obtain the conjugation of the functional. Then the existence of critical point is obtained by mountain pass lemma. Finally, we assert that the critical point of the energy functional is the mild solution of the first order Hamiltonian random impulsive differential equation. Finally, an example is presented to illustrate the feasibility and effectiveness of our results.</p>

scholarly journals Almost Periodic Solutions of First-Order Ordinary Differential Equations

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 171 ◽  
Author(s):  
Seifedine Kadry ◽  
Gennady Alferov ◽  
Gennady Ivanov ◽  
Artem Sharlay
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Upper And Lower Bounds ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
First Order ◽  
Existence And Stability ◽  
Solutions Of Equations ◽  
The Right

Approaches to estimate the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determination for both upper and lower bounds for these solutions are found. The existence and stability of almost periodic problems are studied. The novelty of this paper lies in the fact that the use of apparatus derivatives allows for the reduction of restrictions on the degree of smoothness of the right parts. In the works of Lebedeva [1], regarding the number of periodic solutions of equations first order, they required a high degree of smoothness. Franco et al. required the smoothness of the second derivative of the Schwartz equation [2]. We have all of these restrictions lifted. Our new form presented also emphasizes this novelty.

scholarly journals Positive solutions of differential equations with unbounded Green’s kernel

2012 ◽  
Vol 6 (2) ◽  
pp. 159-173
Author(s):  
John Graef ◽  
Seshadev Padhi ◽  
Smita Pati ◽  
P.K. Kar
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Positive Solutions ◽  
Ecological Model ◽  
Sufficient Conditions ◽  
Allee Effects ◽  
Positive Periodic Solutions ◽  
First Order ◽  
First Order Differential Equations

Sufficient conditions are obtained for the existence/nonexistence of at least two positive periodic solutions of a class of first order differential equations having an unbounded Green?s function. An application to an ecological model with strong Allee effects is also given.

scholarly journals Some notes to existence and stability of the positive periodic solutions for a delayed nonlinear differential equations

2016 ◽  
Vol 14 (1) ◽  
pp. 361-369 ◽  
Author(s):  
Božena Dorociaková ◽  
Rudolf Olach
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Blood Cells ◽  
Delay Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Existence And Stability ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

AbstractThe paper deals with the existence of positive ω-periodic solutions for a class of nonlinear delay differential equations. For example, such equations represent the model for the survival of red blood cells in an animal. The sufficient conditions for the exponential stability of positive ω-periodic solution are also considered.

PERIODIC SOLUTIONS AND BIFURCATIONS OF FIRST-ORDER PERIODIC IMPULSIVE DIFFERENTIAL EQUATIONS

2009 ◽  
Vol 19 (08) ◽  
pp. 2515-2530 ◽  
Author(s):  
ZHAOPING HU ◽  
MAOAN HAN
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Impulsive Differential Equations ◽  
Saddle Node Bifurcation ◽  
First Order ◽  
Double Period ◽  
Saddle Node ◽  
Stability And Bifurcation

In this paper, we use the method of displacement functions to study the existence, stability and bifurcation of periodic solutions of scalar periodic impulsive differential equations. We obtain some new and interesting results on saddle-node bifurcation and double-period bifurcation of periodic solution.

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