scholarly journals A necessary condition for the existence of periodic solutions of certain three dimensional autonomous systems

2009 ◽  
Vol 22 (8) ◽  
pp. 1292-1296 ◽  
Author(s):  
M. Bayat ◽  
B. Mehri
Keyword(s):  
Periodic Solutions ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Necessary Condition ◽  
Existence Of Periodic Solutions

The Necessary Condition for the Existence of Periodic Solutions of Certain Three Dimensional Nonlinear Dynamical Systems

2012 ◽  
Vol 252 ◽  
pp. 40-43
Author(s):  
Ting Ting Quan ◽  
Jing Li ◽  
Min Sun
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Nonlinear Dynamical Systems ◽  
Three Dimensional ◽  
Basic Research ◽  
Necessary Condition ◽  
Nonlinear Dynamical ◽  
Closed Orbits ◽  
Existence Of Periodic Solutions ◽  
Important Significance

In this paper, we investigate a class of three dimensional nonlinear dynamical systems whose unperturbed systems have a family of periodic orbits. Firstly, we establish the moving Frenet Frame on these closed orbits. Secondly, the successor functions are defined by the orbits which go through the normal plane. Finally, by judging the existence of solutions of the equations obtained from the Successor functions, we obtain the necessary condition for the existence of periodic solutions of these three dimensional nonlinear dynamical systems. The result has important significance for the basic research of applied mechanics.

scholarly journals Perturbed generalised Hamiltonian systems and some advection models

1998 ◽  
Vol 57 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Jibin Li ◽  
J.R. Christie ◽  
K. Gopalsamy
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Flow Patterns ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Existence Of Periodic Solutions

In this paper, it is shown that the theory of perturbed generalised Hamiltonian systems provides an effective method for understanding the description of flow patterns of some three-dimensional flows. Firstly, theorems for the persistence of periodic solutions of three-dimensional generalised Hamiltonian systems under perturbation are given by developing Melnikov's method. Then, three different systems of three-dimensional steady fluid flows are discussed and the existence or non-existence of periodic solutions of these systems is proved.

ON 3D HAMILTONIAN SYSTEMS VIA DARBOUX–WEINSTEIN COORDINATES

2009 ◽  
Vol 06 (03) ◽  
pp. 451-459
Author(s):  
RĂZVAN M. TUDORAN ◽  
RAMONA A. TUDORAN
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Three Dimensional ◽  
Stability Of Equilibria ◽  
Existence Of Periodic Solutions ◽  
The Stability

In this paper we are analyzing the stability of equilibria and also the existence of periodic solutions of three dimensional Hamiltonian systems using Darboux–Weinstein coordinates.

KNOTTED PERIODIC SOLUTIONS OF A LINEAR NONAUTONOMOUS SYSTEM AND SOME RELATED THREE-DIMENSIONAL FLOWS

2012 ◽  
Vol 22 (11) ◽  
pp. 1250280
Author(s):  
JIBIN LI ◽  
XIAOHUA ZHAO
Keyword(s):  
Phase Space ◽  
Periodic Solutions ◽  
Periodic Orbits ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Distinct Type ◽  
Frequency Parameter ◽  
Bounded Region ◽  
Nonautonomous Systems ◽  
Dimensional Phase Space

This paper considers a three-dimensional linear nonautonomous systems. It shows that for every integer frequency parameter value, this system has a distinct type of knotted periodic solutions, which lie in a bounded region of R3. Exact explicit parametric representations of the knotted periodic solutions are given. By using these parametric representations, two series of three-dimensional flows are constructed, such that these three-dimensional autonomous systems have knotted periodic orbits in the three-dimensional phase space.

scholarly journals Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Shuang Guo ◽  
Weihua Jiang
Keyword(s):  
Global Stability ◽  
Periodic Solutions ◽  
Three Dimensional ◽  
Growth Time ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
System With Time Delay

A class of three-dimensional Gause-type predator-prey model is considered. Firstly, local stability of equilibrium indicating the extinction of top-predator is obtained. Meanwhile, we construct a Lyapunov function, which is an extension of the Lyapunov functions constructed by Hsu for predator-prey system (2005), to give the global stability of the equilibrium. Secondly, we analyze the stability of coexisting equilibrium of predator-prey system with time delay when the predator catches the prey of pregnancy or with growth time. The delay can lead to periodic solutions, which is consistent with the law of growth for birds and some mammals. Further, an explicit formula is given which determines the stability of the bifurcating periodic solutions theoretically and the existence of periodic solutions is displayed by numerical simulations.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Periodic Solutions of Non-autonomous Allen–Cahn Equations Involving Fractional Laplacian

2020 ◽  
Vol 20 (3) ◽  
pp. 725-737 ◽  
Author(s):  
Zhenping Feng ◽  
Zhuoran Du
Keyword(s):  
Variational Methods ◽  
Periodic Solutions ◽  
Smooth Function ◽  
Fractional Laplacian ◽  
Type Inequality ◽  
Energy Functional ◽  
Large Integer ◽  
Existence Of Periodic Solutions ◽  
Double Well Potential

AbstractWe consider periodic solutions of the following problem associated with the fractional Laplacian: {(-\partial_{xx})^{s}u(x)+\partial_{u}F(x,u(x))=0} in {\mathbb{R}}. The smooth function {F(x,u)} is periodic about x and is a double-well potential with respect to u with wells at {+1} and -1 for any {x\in\mathbb{R}}. We prove the existence of periodic solutions whose periods are large integer multiples of the period of F about the variable x by using variational methods. An estimate of the energy functional, Hamiltonian identity and Modica-type inequality for periodic solutions are also established.

scholarly journals On the equivalence of three-dimensional differential systems

2020 ◽  
Vol 18 (1) ◽  
pp. 1164-1172
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Periodic Systems ◽  
Structural Form ◽  
Differential Systems

Abstract In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.

A New Category of Three-Dimensional Chaotic Flows with Identical Eigenvalues

2020 ◽  
Vol 30 (02) ◽  
pp. 2050026 ◽  
Author(s):  
Zahra Faghani ◽  
Fahimeh Nazarimehr ◽  
Sajad Jafari ◽  
Julien C. Sprott
Keyword(s):  
Chaotic Systems ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Special Property ◽  
Computer Search ◽  
Chaotic Flows ◽  
Stable Equilibria ◽  
Dynamical Properties ◽  
Simple Systems ◽  
First Time

In this paper, some new three-dimensional chaotic systems are proposed. The special property of these autonomous systems is their identical eigenvalues. The systems are designed based on the general form of quadratic jerk systems with 10 terms, and some systems with stable equilibria. Using a systematic computer search, 12 simple chaotic systems with identical eigenvalues were found. We believe that systems with identical eigenvalues are described here for the first time. These simple systems are listed in this paper, and their dynamical properties are investigated.

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