On the Bifurcation Theory of Periodic Solutions of Dynamic Systems with the Simplest Symmetry under Changes of Control Parameters

In this paper, we present a discontinuous cytotoxic T cells (CTLs) response for HTLV-1. Moreover, a delay parameter for the activation of CTLs is considered. In fact, a system of differential equation with discontinuous right-hand side with delay is defined for HTLV-1. For analyzing the dynamical behavior of the system, graphical Hopf bifurcation is used. In general, Hopf bifurcation theory will help to obtain the periodic solutions of a system as parameter varies. Therefore, by applying the frequency domain approach and analyzing the associated characteristic equation, the existence of Hopf bifurcation by using delay immune response as a bifurcation parameter is determined. The stability of Hopf bifurcation periodic solutions is obtained by the Nyquist criterion and the graphical Hopf bifurcation theorem. At the end, numerical simulations demonstrated our results for the system of HTLV-1.

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Analysis of Straight-Line Motion of Towed Ships

Journal of Ship Research ◽

10.5957/jsr.1991.35.4.304 ◽

1991 ◽

Vol 35 (04) ◽

pp. 304-313

Author(s):

Fotis Andrea Papoulias

Keyword(s):

Dynamic Response ◽

Periodic Solutions ◽

Bifurcation Theory ◽

Loss Of Stability ◽

Nonlinear Analyses ◽

Surface Ship ◽

Numerical Integrations ◽

Straight Line ◽

Linear And Nonlinear ◽

Dynamic Loss

The problem of dynamic loss of stability in steady towing of a surface ship is considered. The two coordinates of the towing point and the towline length are the main bifurcation parameters. Bifurcation theory techniques are used in order to compute equilibrium and periodic solutions. The results are confirmed by numerical integrations. It is shown that both linear and nonlinear analyses are required to thoroughly understand, predict, and evaluate the system dynamic response.

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Combat as an Interpersonal Synergy: An Ecological Dynamics Approach to Combat Sports

Sports Medicine ◽

10.1007/s40279-019-01173-y ◽

2019 ◽

Vol 49 (12) ◽

pp. 1825-1836 ◽

Cited By ~ 2

Author(s):

Kai Krabben ◽

Dominic Orth ◽

John van der Kamp

Keyword(s):

Dynamic Systems ◽

Local Level ◽

Control Parameters ◽

Combat Sports ◽

Global Level ◽

Interactive Approach ◽

Ecological Dynamics ◽

Skilled Performance ◽

Initial Support ◽

And Control

Abstract In combat sports, athletes continuously co-adapt their behavior to that of the opponent. We consider this interactive aspect of combat to be at the heart of skilled performance, yet combat sports research often neglects or limits interaction between combatants. To promote a more interactive approach, the aim of this paper is to understand combat sports from the combined perspective of ecological psychology and dynamic systems. Accordingly, combat athletes are driven by perception of affordances to attack and defend. Two combatants in a fight self-organize into one interpersonal synergy, where the perceptions and actions of both athletes are coupled. To be successful in combat, performers need to manipulate and take advantage of the (in)stability of the system. Skilled performance in combat sports therefore requires brinkmanship: combatants need to be aware of their action boundaries and purposefully act in meta-stable regions on the limits of their capabilities. We review the experimental literature to provide initial support for a synergetic approach to combat sports. Expert combatants seem able to accurately perceive action boundaries for themselves and their opponent. Local-level behavior of individual combatants has been found to lead to spatiotemporal synchronization at the global level of a fight. Yet, a formal understanding of combat as a dynamic system starting with the identification of order and control parameters is still lacking. We conclude that the ecological dynamics perspective offers a promising approach to further our understanding of skilled performance in combat sports, as well as to assist coaches and athletes to promote optimal training and learning.

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Inertially Coupled Galloping of Iced Conductors

Journal of Applied Mechanics ◽

10.1115/1.2899419 ◽

1992 ◽

Vol 59 (1) ◽

pp. 140-145 ◽

Cited By ~ 48

Author(s):

P. Yu ◽

A. H. Shah ◽

N. Popplewell

Keyword(s):

Periodic Solutions ◽

Cross Section ◽

Mixed Mode ◽

Bifurcation Theory ◽

Degrees Of Freedom ◽

Center Of Mass ◽

Asymptotic Solutions ◽

Periodic Motions ◽

Two Degrees Of Freedom ◽

First Time

This paper is concerned with the galloping of iced conductors modeled as a two-degrees-of-freedom system. It is assumed that a realistic cross-section of a conductor has eccentricity; that is, its center of mass and elastic axis do not coincide. Bifurcation theory leads to explicit asymptotic solutions not only for the periodic solutions but also for the nonresonant, quasi-periodic motions. Critical boundaries, where bifurcations occur, are described explicitly for the first time. It is shown that an interesting mixed-mode phenomenon, which cannot happen in cocentric cases, may exist even for nonresonance.

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Extracting principal parameters of complex networks

International Journal of Modern Physics C ◽

10.1142/s012918311550103x ◽

2015 ◽

Vol 26 (09) ◽

pp. 1550103

Author(s):

Yifang Ma ◽

Zhiming Zheng

Keyword(s):

Dynamic Systems ◽

Growth Process ◽

Dimensional Space ◽

High Dimensional ◽

Scale Function ◽

Control Parameters ◽

Diffusion Matrix ◽

Similarity Relations ◽

Low Dimensional ◽

Network Ensembles

The evolution of networks or dynamic systems is controlled by many parameters in high-dimensional space, and it is crucial to extract the reduced and dominant ones in low-dimensional space. Here we consider the network ensemble, introduce a matrix resolvent scale function and apply it to a spectral approach to get the similarity relations between each pair of networks. The concept of Diffusion Maps is used to get the principal parameters, and we point out that the reduced dimensional principal parameters are captured by the low order eigenvectors of the diffusion matrix of the network ensemble. We validate our results by using two classical network ensembles and one dynamical network sequence via a cooperative Achlioptas growth process where an abrupt transition of the structures has been captured by our method. Our method provides a potential access to the pursuit of invisible control parameters of complex systems.

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

Advances in Mathematical Physics ◽

10.1155/2021/6689771 ◽

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.

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Bifurcation Theory and Periodic Solutions of Some Autonomous Functional Differential Equations

Dynamical Systems ◽

10.1016/b978-0-12-164902-9.50025-3 ◽

1976 ◽

pp. 99-102

Author(s):

ROGER D. NUSSBAUM

Keyword(s):

Differential Equations ◽

Periodic Solutions ◽

Bifurcation Theory ◽

Functional Differential Equations ◽

Functional Differential

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Further Remarks on the Existence of Periodic Solutions of Linear Time Varying Periodic Fractional Order Systems

Volume 9: 13th ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications ◽

10.1115/detc2017-67903 ◽

2017 ◽

Author(s):

XueFeng Zhang ◽

YangQuan Chen

Keyword(s):

Laplace Transform ◽

Periodic Solutions ◽

Fractional Order ◽

Dynamic Systems ◽

Linear Time ◽

Periodic Systems ◽

Time Varying ◽

Fractional Order Systems ◽

Order Linear ◽

Existence Of Periodic Solutions

Existence of periodic solutions of fractional order dynamic systems is an important and difficult issue in fractional order systems field. In this paper, the non existence of completely periodic solutions and existence of partly periodic solutions of fractional order linear time varying periodic systems and fractional order nonlinear time varying periodic systems are discussed. A new property of Laplace transform of periodic function is derived. The non existences of completely periodic solutions of fractional order linear time varying periodic systems and fractional order nonlinear time varying periodic fractional order systems are presented by Laplace transform method and contradiction approach. The existence of partly periodic solutions of fractional order dynamic systems are proved by constructing numerical examples and considering Laplace transform property approaches. The examples and state figures are given to illustrate the effectiveness of conclusion presented.

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