Birth of bilayered torus and torus breakdown in a piecewise-smooth dynamical system

2006 ◽  
Vol 351 (3) ◽  
pp. 167-174 ◽  
Author(s):  
Zhanybai T. Zhusubaliyev ◽  
Erik Mosekilde
Keyword(s):  
Dynamical System ◽  
Piecewise Smooth ◽  
Torus Breakdown ◽  
Smooth Dynamical System

scholarly journals The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification

Meccanica ◽  
2020 ◽  
Vol 55 (10) ◽  
pp. 1885-1902
Author(s):  
Yang Liu ◽  
Joseph Páez Chávez ◽  
Jiajia Zhang ◽  
Jiyuan Tian ◽  
Bingyong Guo ◽  
...  
Keyword(s):  
Dynamical System ◽  
Mathematical Formulation ◽  
Path Following ◽  
Piecewise Smooth ◽  
Experimental Results ◽  
Scale Down ◽  
Speed Up ◽  
Small Bowel Endoscopy ◽  
Numerical Optimisation ◽  
Smooth Dynamical System

Abstract The vibro-impact capsule system has been studied extensively in the past decade because of its research challenges as a piecewise-smooth dynamical system and broad applications in engineering and healthcare technologies. This paper reports our team’s first attempt to scale down the prototype of the vibro-impact capsule to millimetre size, which is 26 mm in length and 11 mm in diameter, aiming for small-bowel endoscopy. Firstly, an existing mathematical model of the prototype and its mathematical formulation as a piecewise-smooth dynamical system are reviewed in order to carry out numerical optimisation for the prototype by means of path-following techniques. Our numerical analysis shows that the prototype can achieve a high progression speed up to 14.4 mm/s while avoiding the collision between the inner mass and the capsule which could lead to less propulsive force on the capsule so causing less discomfort on the patient. Secondly, the experimental rig and procedure for testing the prototype are introduced, and some preliminary experimental results are presented. Finally, experimental results are compared with the numerical results to validate the optimisation as well as the feasibility of the vibro-impact technique for the potential of a controllable endoscopic procedure.

scholarly journals On choosing state variables for piecewise-smooth dynamical system simulations

2018 ◽  
Vol 95 (2) ◽  
pp. 1165-1188 ◽  
Author(s):  
Jin-Song Pei ◽  
Joseph P. Wright ◽  
François Gay-Balmaz ◽  
James L. Beck ◽  
Michael D. Todd
Keyword(s):  
Dynamical System ◽  
Piecewise Smooth ◽  
State Variables ◽  
Smooth Dynamical System

Sliding in a piecewise-smooth dynamical system with a hold-on effect

2014 ◽  
Vol 378 (42) ◽  
pp. 3085-3092
Author(s):  
Elena Blokhina ◽  
Dimitri Galayko ◽  
Danièle Fournier-Prunaret ◽  
Orla Feely
Keyword(s):  
Dynamical System ◽  
Piecewise Smooth ◽  
Smooth Dynamical System

scholarly journals Multistability in a quasiperiodically forced piecewise smooth dynamical system

2020 ◽  
Vol 84 ◽  
pp. 105165 ◽  
Author(s):  
Gaolei Li ◽  
Yuan Yue ◽  
Jianhua Xie ◽  
Celso Grebogi
Keyword(s):  
Dynamical System ◽  
Piecewise Smooth ◽  
Smooth Dynamical System

scholarly journals Control of near-grazing dynamics in impact oscillators

2005 ◽  
Vol 461 (2063) ◽  
pp. 3365-3380 ◽  
Author(s):  
Harry Dankowicz ◽  
Jenny Jerrelind
Keyword(s):  
Dynamical System ◽  
Nonlinear Oscillator ◽  
Periodic Trajectory ◽  
Piecewise Smooth ◽  
Linear Feedback ◽  
Local Analysis ◽  
Feedback Strategy ◽  
System Parameters ◽  
Impact Oscillators ◽  
Smooth Dynamical System

A method is presented for controlling the persistence of a local attractor near a grazing periodic trajectory in a piecewise smooth dynamical system in the presence of discontinuous jumps in the state associated with intersections with system discontinuities. In particular, it is shown that a discrete, linear feedback strategy may be employed to retain the existence of an attractor near the grazing trajectory, such that the deviation of the attractor from the grazing trajectory goes to zero as the system parameters approach those corresponding to grazing contact. The implementation relies on a local analysis of the near-grazing dynamics using the concept of discontinuity mappings. Numerical results are presented for a linear and a nonlinear oscillator.

scholarly journals Invariant jets of a smooth dynamical system

2001 ◽  
Vol 129 (3) ◽  
pp. 379-448
Author(s):  
Sophie Lemaire
Keyword(s):  
Dynamical System ◽  
Smooth Dynamical System

PERIOD-DOUBLING SCENARIO WITHOUT FLIP BIFURCATIONS IN A ONE-DIMENSIONAL MAP

2005 ◽  
Vol 15 (04) ◽  
pp. 1267-1284 ◽  
Author(s):  
V. AVRUTIN ◽  
M. SCHANZ
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Symmetry Breaking ◽  
Period Doubling ◽  
Pitchfork Bifurcation ◽  
Period Doubling Bifurcation ◽  
Coexisting Attractors ◽  
One Dimensional ◽  
Poincaré Return Map ◽  
Smooth Dynamical System

In this work a one-dimensional piecewise-smooth dynamical system, representing a Poincaré return map for dynamical systems of the Lorenz type, is investigated. The system shows a bifurcation scenario similar to the classical period-doubling one, but which is influenced by so-called border collision phenomena and denoted as border collision period-doubling bifurcation scenario. This scenario is formed by a sequence of pairs of bifurcations, whereby each pair consists of a border collision bifurcation and a pitchfork bifurcation. The mechanism leading to this scenario and its characteristic properties, like symmetry-breaking and symmetry-recovering as well as emergence of coexisting attractors, are investigated.

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