scholarly journals Calculating Floquet Multipliers for Periodic Solution of Non-smooth Dynamical System

2019 ◽  
Author(s):  
De-hong CHEN ◽  
Su-xin XIE ◽  
Xiao-chun HUANG ◽  
Yan-mao CHEN
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Floquet Multipliers ◽  
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

The Generalized Shooting Arc-Length Method for Periodic Solutions and the Corresponding Periods of Nonlinear Dynamical Systems

2001 ◽  
Author(s):  
Dexin Li ◽  
Jianxue Xu
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Periodic Orbit ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Optimization Method ◽  
Arc Length ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Nonlinear Dynamical

Abstract In this paper, a generalized shooting/arc-length method for determining periodic orbit and its period of nonlinear dynamical system is presented. At first, by changing the time scale the period value of periodic orbit of the nonlinear system is drawn into the governing equation of this system. Then, by using the period value as a parameter, the shooting/arc-length procedure is taken for seeking such a periodic solution and its period simultaneously. The value of increment changed in iteration procedure is selected by using optimization method. The procedure involves the detennining of periodic orbit and its period value of the system. Thereby, the periodic orbit and period value of the system can be sought out rapidly and precisely. At last, the validity of such method is verified by determining the periodic orbit and period value for van der pol equation and nonlinear rotor-bear 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.

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

Dynamical Behaviors for a Predator-Prey System with State-Dependent Impulsive Effects

2011 ◽  
Vol 130-134 ◽  
pp. 385-390
Author(s):  
Ling Zhen Dong ◽  
Lan Sun Chen
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Impulsive System ◽  
Impulsive Effects ◽  
Predator Prey ◽  
Dynamical Behaviors ◽  
Prey System ◽  
State Dependent ◽  
Impulsive Model

With some theory about continuous and impulsive dynamical system, an impulsive model based on a special predator-prey system is considered. We assume that the impulsive effects occur when the density of the prey reaches a given value. For such a state-dependent impulsive system, the existence, uniqueness and orbital asymptotic stability of an order-1 periodic solution are discussed. Further, the existence of an order-2 periodic solution is also obtained, and persistence of the system is investigated.

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