Chimera state in a network of nonlocally coupled impact oscillators

2021 ◽  
Vol 22 ◽  
pp. 235-244
Author(s):  
Sajad JAFARI
Keyword(s):  
Chimera State ◽  
Impact Oscillators

Global Analysis of the Double Impact Oscillator Dynamics

1999 ◽  
Author(s):  
František Peterka
Keyword(s):  
Global Analysis ◽  
Impact Oscillator ◽  
System Parameters ◽  
Impact Oscillators ◽  
Real Value ◽  
Simulation Results ◽  
The Impact ◽  
Impact Motion ◽  
Double Impact ◽  
Phase Motion

Abstract The double impact oscillator represents two symmetrically arranged single impact oscillators. It is the model of a forming machine, which does not spread the impact impulses into its neighbourhood. The anti-phase impact motion of this system has the identical dynamics as the single system. The in-phase motion and the influence of asymmetries of the system parameters are studied using numerical simulations. Theoretical and simulation results are verified experimentally and the real value of the restitution coefficient is determined by this method.

Non-Smooth Dynamics and Non-Classical Bifurcations in Impulse-Impact Oscillators

1999 ◽  
Author(s):  
Stefano Lenci ◽  
Giuseppe Rega
Keyword(s):  
Local Level ◽  
Basins Of Attraction ◽  
Dynamical Regime ◽  
Impact Oscillator ◽  
Stable And Unstable Manifolds ◽  
Impact Oscillators ◽  
Unstable Manifolds ◽  
Local And Global Bifurcations ◽  
Initial Description ◽  
Smooth Dynamics

Abstract Some aspects of the nonlinear dynamics of an impulse-impact oscillator are investigated. After an initial description of the prototype mechanical model used to illustrate the results, attention is paid to the classical local and global bifurcations which are at the base of the changes of dynamical regime. Some non-classical phenomena due to the particular nature of the investigated system are then considered. At a local level, it is shown that periodic solutions may appear (or disappear) through a non-classical bifurcation which involves synchronization of impulses and impacts. Similarities and differences with the classical bifurcations are discussed. At a global level, the effects of the non-continuity of the orbits in the phase space on the basins of attraction topology are investigated. It is shown how this property is at the base of a non-classical homoclinic bifurcation where the homoclinic points disappear after the first touch between the stable and unstable manifolds.

scholarly journals Synchrony in networks of Franklin bells

2019 ◽  
Vol 84 (5) ◽  
pp. 1001-1021 ◽  
Author(s):  
Mustafa Şayli ◽  
Yi Ming Lai ◽  
Rüdiger Thul ◽  
Stephen Coombes
Keyword(s):  
Linear Stability ◽  
Benjamin Franklin ◽  
Stability Function ◽  
Impact Oscillators ◽  
Network Topologies ◽  
Network States ◽  
Low Dimensional ◽  
Oscillatory Network ◽  
The Impact ◽  
Theoretical Results

Abstract The Franklin bell is an electro-mechanical oscillator that can generate a repeating chime in the presence of an electric field. Benjamin Franklin famously used it as a lightning detector. The chime arises from the impact of a metal ball on a metal bell. Thus, a network of Franklin bells can be regarded as a network of impact oscillators. Although the number of techniques for analysing impacting systems has grown in recent years, this has typically focused on low-dimensional systems and relatively little attention has been paid to networks. Here we redress this balance with a focus on synchronous oscillatory network states. We first study a single Franklin bell, showing how to construct periodic orbits and how to determine their linear stability and bifurcation. To cope with the non-smooth nature of the impacts we use saltation operators to develop the correct Floquet theory. We further introduce a new smoothing technique that circumvents the need for saltation and that recovers the saltation operators in some appropriate limit. We then consider the dynamics of a network of Franklin bells, showing how the master stability function approach can be adapted to treat the linear stability of the synchronous state for arbitrary network topologies. We use this to determine conditions for network induced instabilities. Direct numerical simulations are shown to be in excellent agreement with theoretical results.

Chaotic attractor of the normal form map for grazing bifurcations of impact oscillators

2019 ◽  
Vol 398 ◽  
pp. 164-170 ◽  
Author(s):  
Pengcheng Miao ◽  
Denghui Li ◽  
Yuan Yue ◽  
Jianhua Xie ◽  
Celso Grebogi
Keyword(s):  
Normal Form ◽  
Chaotic Attractor ◽  
Impact Oscillators ◽  
Grazing Bifurcations
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