Stochastic Bifurcations, Chaos and Phantom Attractors in the Langford System with Tori

2020 ◽  
Vol 30 (16) ◽  
pp. 2030051
Author(s):  
Irina Bashkirtseva ◽  
Lev Ryashko
Keyword(s):  
Dynamic Model ◽  
Gaussian Noise ◽  
Stochastic Dynamics ◽  
Three Dimensional ◽  
Stochastic Generation ◽  
Noise Amplification ◽  
Quasiperiodic Oscillations ◽  
Stochastic Bifurcations

The variability of stochastic dynamics for a three-dimensional dynamic model in a parametric zone with 2-tori is investigated. It is shown how weak Gaussian noise transforms deterministic quasiperiodic oscillations into noisy bursting. The phenomenon of stochastic generation of a phantom attractor and its shift with noise amplification is revealed. This phenomenon, accompanied by order-chaos transitions, is studied in terms of stochastic [Formula: see text]- and [Formula: see text]-bifurcations.

scholarly journals Stochastic Bifurcations and Noise-Induced Chaos in 3D Neuron Model

2016 ◽  
Vol 26 (12) ◽  
pp. 1630032 ◽  
Author(s):  
Irina Bashkirtseva ◽  
Sergei Fedotov ◽  
Lev Ryashko ◽  
Evdokia Slepukhina
Keyword(s):  
Stochastic Dynamics ◽  
Stable Equilibrium ◽  
Deterministic Model ◽  
Three Dimensional ◽  
Random Disturbances ◽  
Stable Equilibria ◽  
Relationship Of ◽  
Stochastic Bifurcations ◽  
Good Agreement ◽  
Qualitative Changes

The stochastically forced three-dimensional Hindmarsh–Rose model of neural activity is considered. We study the effect of random disturbances in parametric zones where the deterministic model exhibits mono- and bistable dynamic regimes with period-adding bifurcations of oscillatory modes. It is shown that in both cases the phenomenon of noise-induced bursting is observed. In the monostable zone, where the only attractor of the system is a stable equilibrium, this effect is connected with a stochastic generation of large-amplitude oscillations due to the high excitability of the model. In a parametric zone of coexisting stable equilibria and limit cycles, bursts appear due to noise-induced transitions between the attractors. For a quantitative analysis of the noise-induced bursting and corresponding stochastic bifurcations, an approach based on the stochastic sensitivity function (SSF) technique is applied. Our estimations of the strength of noise that generates such qualitative changes in stochastic dynamics are in a good agreement with the direct numerical simulation. A relationship of the noise-induced generation of bursts with transitions from order to chaos is discussed.

A Three-Dimensional Dynamic Model of Startup Heating during Induction Melting in a Cold Crucible

2021 ◽  
Vol 92 (3) ◽  
pp. 150-153
Author(s):  
I. N. Skrigan ◽  
D. B. Lopukh ◽  
A. V. Vavilov ◽  
A. P. Martynov
Keyword(s):  
Dynamic Model ◽  
Three Dimensional ◽  
Induction Melting ◽  
Cold Crucible

Force-based delay compensation for hardware-in-the-loop simulation divergence of 6-DOF space contact

2017 ◽  
Vol 233 (1) ◽  
pp. 151-165
Author(s):  
Qian Wang ◽  
Chenkun Qi ◽  
Feng Gao ◽  
Xianchao Zhao ◽  
Anye Ren ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Dynamic Models ◽  
Contact Process ◽  
Three Dimensional ◽  
Compensation Method ◽  
Degree Of Freedom ◽  
Hardware In The Loop ◽  
Delay Compensation ◽  
Measurement Delay ◽  
Six Degree Of Freedom

The contact process of a space docking device needs verification before launching. The verification cannot only rely on the software simulation since the contact dynamic models are not accurate enough yet, especially when the geometric shape of the device is complex. Hardware-in-the-loop simulation is a choice to perform the ground test, where the contact dynamic model is replaced by a real device and the real contact occurs. However, the Hardware-in-the-loop simulation suffers from energy increase and instability since time delay is unavoidable. The existing delay compensation methods are mainly focused on a uniaxial or three-dimensional contact. In this paper, a force-based delay compensation method is proposed for the hardware-in-the-loop simulation of a six degree-of-freedom space contact. A six degree-of-freedom dynamic model of the spacecraft motion is derived, and a six degree-of-freedom delay compensation method is proposed. The delay is divided into track delay and measurement delay, which are compensated individually. Experiment results show that the proposed delay compensation method is effective for the six degree-of-freedom space contact.

Fully Coupled Three-Dimensional Dynamic Response of a TLP Floating Wind Turbine in Waves and Wind

2012 ◽  
Author(s):  
G. K. V. Ramachandran ◽  
H. Bredmose ◽  
J. N. Sørensen ◽  
J. J. Jensen
Keyword(s):  
Wind Turbine ◽  
Dynamic Model ◽  
Three Dimensional ◽  
Geographic Location ◽  
Climatic Conditions ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Total System ◽  
Wave Loads ◽  
Aerodynamic Loads

A dynamic model for a tension-leg platform (TLP) floating offshore wind turbine is proposed. The model includes three-dimensional wind and wave loads and the associated structural response. The total system is formulated using 17 degrees of freedom (DOF), 6 for the platform motions and 11 for the wind turbine. Three-dimensional hydrodynamic loads have been formulated using a frequency- and direction-dependent spectrum. While wave loads are computed from the wave kinematics using Morison’s equation, aerodynamic loads are modelled by means of unsteady Blade-Element-Momentum (BEM) theory, including Glauert correction for high values of axial induction factor, dynamic stall, dynamic wake and dynamic yaw. The aerodynamic model takes into account the wind shear and turbulence effects. For a representative geographic location, platform responses are obtained for a set of wind and wave climatic conditions. The platform responses show an influence from the aerodynamic loads, most clearly through a quasi-steady mean surge and pitch response associated with the mean wind. Further, the aerodynamic loads show an influence from the platform motion through more fluctuating rotor loads, which is a consequence of the wave-induced rotor dynamics. In the absence of a controller scheme for the wind turbine, the rotor torque fluctuates considerably, which induces a growing roll response especially when the wind turbine is operated nearly at the rated wind speed. This can be eliminated either by appropriately adjusting the controller so as to regulate the torque or by optimizing the floater or tendon dimensions, thereby limiting the roll motion. Loads and coupled responses are predicted for a set of load cases with different wave headings. Based on the results, critical load cases are identified and discussed. As a next step (which is not presented here), the dynamic model for the substructure is therefore being coupled to an advanced aero-elastic code Flex5, Øye (1996), which has a higher number of DOFs and a controller module.

Study of a synchronizer mechanism through multibody dynamic analysis

2018 ◽  
Vol 233 (6) ◽  
pp. 1601-1613 ◽  
Author(s):  
Ali Farokhi Nejad ◽  
Giorgio Chiandussi ◽  
Vincenzo Solimine ◽  
Andrea Serra
Keyword(s):  
Dynamic Model ◽  
Three Dimensional ◽  
Time Estimation ◽  
Test Rig ◽  
Operational Conditions ◽  
Multibody Dynamic ◽  
Dynamic Analyses ◽  
Single Cone ◽  
Good Agreement ◽  
Numerical Approaches

The synchronizer mechanism represents the essential component in manual, automatic manual, and dual-clutch transmissions. This paper describes a multibody dynamic model for analysis of a synchronizer mechanism subjected to different operational conditions. The three-dimensional multi-dynamic model is developed to predict the dynamic response of synchronizer, especially for calculation of synchronization time. For the purpose of validation, three different synchronizers (single-cone, double-cone, and triple-cone synchronizers) were used on the test rig machine. For the purpose of synchronizing time estimation, an analytical formulation is proposed. The results of the analytical and multibody dynamic analyses were compared with the experimental data, showing a good agreement. The results of analytical and numerical approaches show that the predicted time of synchronization is more precise than previous works. A sensitivity analysis was performed on the single-cone synchronizer, and the effect of tolerance dimension on the dynamic behavior of the synchronizer was reported.

scholarly journals Stochastic dynamics of planar magnetic moments in a three-dimensional environment

2018 ◽  
Vol 510 ◽  
pp. 98-109 ◽  
Author(s):  
Zochil González Arenas ◽  
Daniel G. Barci ◽  
Miguel Vera Moreno
Keyword(s):  
Stochastic Dynamics ◽  
Magnetic Moments ◽  
Three Dimensional
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