ON SWITCHABILITY OF A FLOW TO THE BOUNDARY IN A PERIODICALLY EXCITED DISCONTINUOUS DYNAMICAL SYSTEM

2008 ◽  
Author(s):  
ALBERT C. J. LUO ◽  
BRANDON M. RAPP
Keyword(s):  
Dynamical System ◽  
Discontinuous Dynamical System

Periodic Motions With Grazing in a Discontinuous Dynamical System With Two Circular Boundaries

2019 ◽  
Author(s):  
Siyu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Periodic Motion ◽  
Necessary Conditions ◽  
Periodic Motions ◽  
Discontinuous System ◽  
Discontinuous Dynamical System ◽  
Sufficient And Necessary Conditions

Abstract In this paper, studied are periodic motions with grazing in a discontinuous dynamical system with two circular boundaries. The grazing motion is for a periodic motion switching to another periodic motions. Thus, the sufficient and necessary conditions of motion switching, grazing and sliding on the boundaries are discussed first. Periodic motions with grazing in the discontinuous system are presented for illustration of motions switching.

Analytical Predication of Complex Motion of a Ball in a Periodically Shaken Horizontal Impact Pair

2011 ◽  
Vol 7 (2) ◽  
Author(s):  
Yu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Bifurcation Analysis ◽  
Periodic Motion ◽  
Analytical Prediction ◽  
Periodic Excitation ◽  
Complex Motion ◽  
Chaotic Motions ◽  
Discontinuous Dynamical System ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis

In this paper, complex motions of a ball in the horizontal impact pair with a periodic excitation are studied analytically using the theory of discontinuous dynamical system. Analytical conditions for motion switching caused by impacts are developed, and generic mapping structures are introduced to describe different periodic and chaotic motions. Analytical prediction of complex periodic motion of the ball in the periodically shaken impact pair is completed, and the corresponding stability and bifurcation analysis are also carried out. Numerical illustrations of periodic and chaotic motions are given.

Global Analysis on a Discontinuous Dynamical System

2017 ◽  
Vol 27 (05) ◽  
pp. 1750078 ◽  
Author(s):  
Hebai Chen ◽  
Zhenbang Cao ◽  
Denghui Li ◽  
Jianhua Xie
Keyword(s):  
Dynamical System ◽  
Global Analysis ◽  
Melnikov Method ◽  
Melnikov Function ◽  
Asymptotically Stable ◽  
Subharmonic Solution ◽  
Abstract Function ◽  
Numerical Examples ◽  
Harmonic Solution ◽  
Discontinuous Dynamical System

We have studied a Filippov system [Formula: see text] with small [Formula: see text], [Formula: see text] and [Formula: see text] being periodic. Since [Formula: see text] is an abstract function, the subharmonic Melnikov function cannot be computed. In other words, for this system the Melnikov method loses effectiveness. First, we proved that the equation has a unique harmonic solution, a unique [Formula: see text]-subharmonic solution for any [Formula: see text] and they are Lyapunov asymptotically stable. Moreover, this equation has no other type of periodic solutions. Further, the attractor of this system is not chaotic. Finally, some numerical examples are given.

Dynamic Properties of the Predator–Prey Discontinuous Dynamical System

2012 ◽  
Vol 67 (1-2) ◽  
pp. 57-60 ◽  
Author(s):  
Ahmed M. A. El-Sayed ◽  
Mohamed E. Nasr
Keyword(s):  
Dynamical System ◽  
Global Stability ◽  
Existence And Uniqueness ◽  
Dynamic Properties ◽  
Equilibrium Points ◽  
Stable Solution ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Discontinuous Dynamical System

In this work, we study the dynamic properties (equilibrium points, local and global stability, chaos and bifurcation) of the predator-prey discontinuous dynamical system. The existence and uniqueness of uniformly Lyapunov stable solution will be proved

scholarly journals Analysis of Discontinuous Dynamical Behaviors of a Friction-Induced Oscillator with an Elliptic Control Law

2018 ◽  
Vol 2018 ◽  
pp. 1-33 ◽  
Author(s):  
Jinjun Fan ◽  
Ping Liu ◽  
Tianyi Liu ◽  
Shan Xue ◽  
Zhaoxia Yang
Keyword(s):  
Dynamical System ◽  
Vector Fields ◽  
Control Law ◽  
Periodic Motions ◽  
Separation Boundary ◽  
Discontinuous System ◽  
Dynamical Behaviors ◽  
Discontinuous Dynamical System ◽  
Discontinuous Boundary ◽  
Mass Spring

This paper develops the passability conditions of flow to the discontinuous boundary and the sticking or sliding and grazing conditions to the separation boundary in the discontinuous dynamical system of a friction-induced oscillator with an elliptic control law and the friction force acting on the mass M through the analysis of the corresponding vector fields and G-functions. The periodic motions of such a discontinuous system are predicted analytically through the mapping structure. Finally, the numerical simulations are given to illustrate the analytical results of motion for a better understanding of physics of motion in the mass-spring-damper oscillator.

Periodic Motions in a Discontinuous Dynamical System With Two Circular Boundaries

2019 ◽  
Author(s):  
Siyu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Periodic Motions ◽  
Discontinuous Dynamical System ◽  
Mapping Structures

Abstract In this paper, periodic motions in a discontinuous dynamical systems are studied. The discontinuous dynamical system has three domains partitioned through two circular boundaries. On the three domains, there are three distinct dynamical systems. From the G-functions, the switchability conditions of a flow from one domain to anther domain at the boundary are developed. The flow mappings from a boundary to a bounbary are developed for each domain and boundary. From the mapping structures, periodic motions in the discontinuous dynamical system are predicted. Numerical simulations of periodic motions and motion switchability at boundaries are presented in the discontinuous dynamical system.

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