Analysis of periodic solutions of a continuous dynamical system with delay and pumping

2009 ◽  
Vol 45 (2) ◽  
pp. 168-174
Author(s):  
A. A. Seslavin
Keyword(s):  
Dynamical System ◽  
Periodic Solutions ◽  
Continuous Dynamical System ◽  
System With Delay

Index Evaluation for Dynamical Systems and Its Application to Locating All the Zeros of a Vector Function

1983 ◽  
Vol 50 (4a) ◽  
pp. 858-862 ◽  
Author(s):  
C. S. Hsu ◽  
R. S. Guttalu
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Periodic Solutions ◽  
Vector Function ◽  
Evaluation Method ◽  
Point Mapping ◽  
Strongly Nonlinear ◽  
Index Evaluation

An index evaluation method is discussed in this paper. It can also serve as the basis of a procedure to locate all the zeros of a vector function. An application of the procedure is made to a strongly nonlinear point-mapping dynamical system in order to locate all the periodic solutions of period one and period two, 41 in total number.

Existence of periodic solutions for sublinear second order dynamical system with (q, p)-Laplacian

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Xiaoxia Yang ◽  
Haibo Chen
Keyword(s):  
Dynamical System ◽  
Saddle Point ◽  
Periodic Solutions ◽  
Existence Theorems ◽  
Second Order ◽  
Saddle Point Theorem ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Existence Of Periodic Solutions

AbstractIn this paper, some existence theorems are obtained for periodic solutions of second order dynamical system with (q, p)-Laplaician by using the least action principle and the saddle point theorem. Our results improve Pasca and Tang’ results.

scholarly journals Stability of a time discrete perturbed dynamical system with delay

1999 ◽  
Vol 3 (1) ◽  
pp. 57-63 ◽  
Author(s):  
Michael I. Gil' ◽  
Sui Sun Cheng
Keyword(s):  
Dynamical System ◽  
Positive Integer ◽  
Difference Equation ◽  
Absolute Stability ◽  
Nonlinear Difference Equation ◽  
Stability Conditions ◽  
System With Delay ◽  
Equation With Delay

LetCnbe the set ofncomplex vectors endowed with a norm‖⋅‖Cn. LetA,Bbe two complexn×nmatrices andτa positive integer. In the present paper we consider the nonlinear difference equation with delay of the typeuk+1=Auk+Buk−τ+Fk(uk,uk−τ),      k=0,1,2,…, whereFk:Cn×Cn→Cnsatisfies the condition‖Fk(x,y)‖Cn≤p‖x‖Cn+q‖y‖Cn,       k=0,1,2,…, wherepandqare positive constants. In this paper, absolute stability conditions for this equation are established.

scholarly journals Periodic Peakon and Smooth Periodic Solutions for KP-MEW(3,2) Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Junning Cai ◽  
Minzhi Wei ◽  
Liping He
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Dynamical Systems ◽  
Periodic Solutions ◽  
Phase Portrait ◽  
Traveling Wave ◽  
Bifurcation Theory ◽  
Wave System ◽  
Integral Constant ◽  
Straight Line

In this paper, we consider the KP-MEW(3,2) equation by the bifurcation theory of dynamical systems when integral constant is considered. The corresponding traveling wave system is a singular planar dynamical system with one singular straight line. The phase portrait for c < 0 , 0 < c < 1 , and c > 1 is drawn. Exact parametric representations of periodic peakon solutions and smooth periodic solution are presented.

scholarly journals Spectrum of continuous two-contours system

2019 ◽  
Vol 24 ◽  
pp. 01014 ◽  
Author(s):  
Alexander G. Tatashev ◽  
Marina V. Yashina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Common Point ◽  
Continuous Dynamical System ◽  
Point Node ◽  
System States

A deterministic continuous dynamical system is considered. This system contains two contours. The length of theith contour equalsci,i= 1, 2. There is a moving segment (cluster) on each contour. The length of the cluster, located on theith contour, equalsli,i= 1, 2. If a cluster moves without delays, then the velocity of the cluster is equal to 1. There is a common point (node) of the contours. Clusters cannot cross the node simultaneously, and therefore delays of clusters occur. A set of repeating system states is called a spectral cycle. Spectral cycles and values of average velocities of clusters have been found. The system belongs to a class of contour systems. This class of dynamical systems has been introduced and studied by A.P. Buslaev.

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