INVESTIGATION OF THE INFLUENCE OF RANDOM PERTURBATIONS ON THE DYNAMICS OF THE SYSTEM IN THE SUSLOV PROBLEM

2021 ◽  
pp. 17-29
Author(s):  
E.A. Mikishanina ◽  
Keyword(s):  
Software Package ◽  
Strange Attractors ◽  
Phase Portraits ◽  
Deterministic System ◽  
Random Perturbations ◽  
Variable Parameters ◽  
Suslov Problem ◽  
Perturbed System ◽  
System A ◽  
Dynamical Regimes

The paper considers the generalized Suslov problem with variable parameters and the influence of random perturbations on the dynamics of the system under consideration. The physical meaning of the Suslov problem is Chaplygin's sleigh, which moves along the inner side of the circle. In the case of a deterministic system, a brief review of the previously obtained results is made, the presence of chaotic dynamics in the system and such effects as the appearance of a strange attractor and noncompact (escaping) trajectories is shown. Moreover, the latter may indicate a possible acceleration in the system. The appearance of chaotic strange attractors occurs due to a cascade of bifurcations of doubling the period. We also consider the dynamics of a perturbed system which arises due to the addition of «white noise» modeled by the Wiener process to one of the equations. Changes in the dynamics of a perturbed system compared to an unperturbed one are studied: chaotization of periodic regimes, the appearance of noncompact trajectories, and the premature destruction of strange attractors. In this paper, phase portraits, maps for the period, graphs of system solutions, and a chart of dynamical regimes are constructed using the Maple software package and the software package «Computer Dynamics: Chaos» (/http://site4.ics.org.ru//chaos_pack).

Dynamics of the suslov problem in a gravitational field: Reversal and strange attractors

2015 ◽  
Vol 20 (5) ◽  
pp. 605-626 ◽  
Author(s):  
Ivan A. Bizyaev ◽  
Alexey V. Borisov ◽  
Alexey O. Kazakov
Keyword(s):  
Gravitational Field ◽  
Strange Attractors ◽  
Field Reversal ◽  
Suslov Problem

DCEL

1998 ◽  
Vol 08 (05n06) ◽  
pp. 619-636 ◽  
Author(s):  
Gill Barequet
Keyword(s):  
Software Package ◽  
Geometric Algorithms ◽  
Programming Environment ◽  
Polyhedral Surfaces ◽  
System A ◽  
Fast Prototyping

In this paper we describe the DCEL system: a geometric software package which implements a polyhedral programming environment. This package enables fast prototyping of geometric algorithms for polyhedra or for polyhedral surfaces. We provide an overview of the system's functionality and demonstrate its use in several applications.

scholarly journals Designing a Tracked Running Gear of a Radio-Controlled Harvester

2020 ◽  
Vol 329 ◽  
pp. 05001
Author(s):  
Vladislav Klubnichkin ◽  
Evgeny Klubnichkin ◽  
Maxim Yakovlev ◽  
Vladimir Makarov ◽  
Vladimir Belyakov
Keyword(s):  
Software Package ◽  
Variable Parameters ◽  
Tracked Vehicles ◽  
Tractive Effort ◽  
Applied Software ◽  
Basic Characteristics ◽  
Universal Mechanism ◽  
Selection Of

This work describes a model of a running gear of the designed tracked radio-controlled harvester intended for clean cutting which has been developed in the applied software package “Universal Mechanism” with use of the “Tracked Vehicles” module. It offers basic characteristics, justifies selection of variable parameters of the model. It describes modelling options of a model travel over variable irregularities, presents the obtained tractive effort torques on sprockets and loads acting on the support rollers.

scholarly journals Random Dynamical Systems Generated by Two Allee Maps

2017 ◽  
Vol 27 (08) ◽  
pp. 1750117
Author(s):  
Jozef Kováč ◽  
Katarína Janková
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Random Dynamical Systems ◽  
Deterministic System ◽  
Random Perturbations ◽  
Small Random Perturbations

In this paper, we study random dynamical systems generated by two Allee maps. Two models are considered — with and without small random perturbations. It is shown that the behavior of the systems is very similar to the behavior of the deterministic system if we use strictly increasing Allee maps. However, in the case of unimodal Allee maps, the behavior can dramatically change irrespective of the initial conditions.

Multistability and Bubbling Route to Chaos in a Deterministic Model for Geomagnetic Field Reversals

2019 ◽  
Vol 29 (12) ◽  
pp. 1930034
Author(s):  
Paulo C. Rech ◽  
Sudarshan Dhua ◽  
N. C. Pati
Keyword(s):  
Fixed Point ◽  
Geomagnetic Field ◽  
Deterministic Model ◽  
Initial Conditions ◽  
Period Doubling ◽  
Basins Of Attraction ◽  
Phase Portraits ◽  
Multiple Attractors ◽  
System A ◽  
Two Parameters

We report coexisting multiple attractors and birth of chaos via period-bubbling cascades in a model of geomagnetic field reversals. The model system comprises a set of three coupled first-order quadratic nonlinear equations with three control parameters. Up to seven kinds of multistable attractors, viz. fixed point-periodic, fixed point-chaotic, periodic–periodic, periodic-chaotic, chaotic–chaotic, fixed point-periodic–periodic, fixed point-periodic-chaotic are obtained depending on the initial conditions for critical parameter sets. Antimonotonicity is a striking characteristic feature of nonlinear systems through which a full Feigenbaum tree corresponding to creation and annihilation of period-doubling cascades is developed. By analyzing the two-parameters dependent dynamics of the system, a critical biparameter zone is identified, where antimonotonicity comes into existence. The complex dynamical behaviors of the system are explored using phase portraits, bifurcation diagrams, Lyapunov exponents, isoperiodic diagram, and basins of attraction.

Design for Manufacture Using a CAD/CAM System—A Methodology for Turned Parts

1983 ◽  
Vol 197 (3) ◽  
pp. 187-195 ◽  
Author(s):  
J C S Plummer ◽  
R G Hannam
Keyword(s):  
Design Process ◽  
Machine Tools ◽  
Software Package ◽  
Design Methodology ◽  
Raw Material ◽  
Design Stage ◽  
Design For Manufacture ◽  
System A ◽  
Cad Cam ◽  
Turned Parts

This paper describes a design methodology which has been developed to ensure that turned parts are designed for manufacture. The methodology has been incorporated in a software package which is used interactively on a CAD/CAM system. The methodology ensures that the choices offered to a designer during the design stage are such that turned parts can be produced to company standards using the manufacturing facilities available. The software package automatically selects the necessary raw material, the appropriate tool assemblies, and the necessary machine tools required to manufacture each component as its design process is carried out.

scholarly journals Three-Dimensional Memristive Hindmarsh–Rose Neuron Model with Hidden Coexisting Asymmetric Behaviors

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Bocheng Bao ◽  
Aihuang Hu ◽  
Han Bao ◽  
Quan Xu ◽  
Mo Chen ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Electromagnetic Induction ◽  
Neuron Model ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Neuronal System ◽  
System A ◽  
Dynamical Behaviors ◽  
Electrical Activities

Since the electrical activities of neurons are closely related to complex electrophysiological environment in neuronal system, a novel three-dimensional memristive Hindmarsh–Rose (HR) neuron model is presented in this paper to describe complex dynamics of neuronal activities with electromagnetic induction. The proposed memristive HR neuron model has no equilibrium point but can show hidden dynamical behaviors of coexisting asymmetric attractors, which has not been reported in the previous references for the HR neuron model. Mathematical model based numerical simulations for hidden coexisting asymmetric attractors are performed by bifurcation analyses, phase portraits, attraction basins, and dynamical maps, which just demonstrate the occurrence of complex dynamical behaviors of electrical activities in neuron with electromagnetic induction. Additionally, circuit breadboard based experimental results well confirm the numerical simulations.

Generating Four-Wing Hyperchaotic Attractor and Two-Wing, Three-Wing, and Four-Wing Chaotic Attractors in 4D Memristive System

2017 ◽  
Vol 27 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Ling Zhou ◽  
Chunhua Wang ◽  
Lili Zhou
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Hyperchaotic System ◽  
Multiple Attractors ◽  
System A ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Line Of Equilibria

By adding only one smooth flux-controlled memristor into a three-dimensional (3D) pseudo four-wing chaotic system, a new real four-wing hyperchaotic system is constructed in this paper. It is interesting to see that this new memristive chaotic system can generate a four-wing hyperchaotic attractor with a line of equilibria. Moreover, it can generate two-, three- and four-wing chaotic attractors with the variation of a single parameter which denotes the strength of the memristor. At the same time, various coexisting multiple attractors (e.g. three-wing attractors, four-wing attractors and attractors with state transition under the same system parameters) are observed in this system, which means that extreme multistability arises. The complex dynamical behaviors of the proposed system are analyzed by Lyapunov exponents (LEs), phase portraits, Poincaré maps, and time series. An electronic circuit is finally designed to implement the hyperchaotic memristive system.

scholarly journals Correcting for Naturally Occurring Mass Isotopologue Abundances in Stable-Isotope Tracing Experiments with PolyMID

Metabolites ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 310
Author(s):  
Heesoo Jeong ◽  
Yan Yu ◽  
Henrik J. Johansson ◽  
Frank C. Schroeder ◽  
Janne Lehtiö ◽  
...  
Keyword(s):  
Stable Isotope ◽  
Metabolic Pathway ◽  
Software Package ◽  
High Mass ◽  
Isotope Tracing ◽  
Mass Spectrometers ◽  
System A ◽  
Naturally Occurring ◽  
High Mass Resolution ◽  
Resolution Mass

Stable-isotope tracing is a method to measure intracellular metabolic pathway utilization by feeding a cellular system a stable-isotope-labeled tracer nutrient. The power of the method to resolve differential pathway utilization is derived from the enrichment of metabolites in heavy isotopes that are synthesized from the tracer nutrient. However, the readout is complicated by the presence of naturally occurring heavy isotopes that are not derived from the tracer nutrient. Herein we present an algorithm, and a tool that applies it (PolyMID-Correct, part of the PolyMID software package), to computationally remove the influence of naturally occurring heavy isotopes. The algorithm is applicable to stable-isotope tracing data collected on low- and high- mass resolution mass spectrometers. PolyMID-Correct is open source and available under an MIT license.

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