scholarly journals Dynamical Behaviors of Coupled Memristor-Based Oscillators with Identical and Different Nonlinearities

2018 ◽  
Vol 2018 ◽  
pp. 1-20
Author(s):  
A. Elsonbaty ◽  
A. Abdelkhalek ◽  
A. Elsaid
Keyword(s):  
Mathematical Models ◽  
Coupled Oscillators ◽  
Perturbation Methods ◽  
Normal Forms ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Two Dimensional ◽  
Numerical Techniques ◽  
Ring Configuration ◽  
Dynamical Behaviors

In this work, the interesting dynamics of coupled nonlinear memristor-based oscillators in ring configuration are explored. The mathematical models are derived to describe the possible cases of employing identical or different nonlinearities. Analytical and numerical techniques, involving perturbation methods, normal forms, phase portraits, and Lyapunov exponents are used to investigate various types of dynamical behaviors along with their stability regions in parameters space. The effects of time-delayed coupling on the proposed system are numerically studied. It is demonstrated that the coupled oscillators show rich dynamics including periodic orbits, quasiperiodicity, two-dimensional, and three-dimensional tori.

Three-Dimensional Dynamic Modeling of the Human Knee to Include Tibio-Femoral and Patello-Femoral Joints

2001 ◽  
Author(s):  
Dumitru Caruntu ◽  
Mohamed Samir Hefzy
Keyword(s):  
Knee Joint ◽  
Mathematical Models ◽  
Dynamic Modeling ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Human Knee ◽  
Two Dimensional Model ◽  
Rigid Contact ◽  
Locomotor Activities

Abstract Most of the anatomical mathematical models that have been developed to study the human knee are either for the tibio-femoral joint (TFJ) or patello-femoral joint (PFJ). Also, most of these models are static or quasistatic, and therefore do not predict the effects of dynamic inertial loads, which occur in many locomotor activities. The only dynamic anatomical model that includes both joints is a two-dimensional model by Tumer and Engin [1]. The model by Abdel-Rahman and Hefzy [2] is the only three dimensional dynamic model for the knee joint available in the literature; yet, it includes only the TFJ and allows only for rigid contact.

scholarly journals On the correctness of mathematical models of time-of-flight cathodoluminescence of direct-gap semiconductors

2019 ◽  
Vol 30 ◽  
pp. 07014
Author(s):  
Mikhail A. Stepovich ◽  
Dmitry V. Turtin ◽  
Elena V. Seregina ◽  
Veronika V. Kalmanovich
Keyword(s):  
Electron Beam ◽  
Gallium Nitride ◽  
Initial Data ◽  
Mathematical Models ◽  
Single Crystal ◽  
Three Dimensional ◽  
Time Of Flight ◽  
Semiconductor Material ◽  
Two Dimensional ◽  
Cathodoluminescence Intensity

Two-dimensional and three-dimensional mathematical models of diffusion and cathodoluminescence of excitons in single-crystal gallium nitride excited by a pulsating sharply focused electron beam in a homogeneous semiconductor material are compared. The correctness of these models has been carried out, estimates have been obtained to evaluate the effect of errors in the initial data on the distribution of the diffusing excitons and the cathodoluminescence intensity.

scholarly journals Analysis of spatial thermal field in a magnetic bearing

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 52-56
Author(s):  
Dawid Wajnert ◽  
Bronisław Tomczuk
Keyword(s):  
Temperature Field ◽  
Mathematical Models ◽  
Computer Simulations ◽  
Thermal Field ◽  
Three Dimensional ◽  
Magnetic Bearing ◽  
Field Analysis ◽  
Two Dimensional ◽  
Temperature Distributions ◽  
Dimensional Simulation

AbstractThis paper presents two mathematical models for temperature field analysis in a new hybrid magnetic bearing. Temperature distributions have been calculated using a three dimensional simulation and a two dimensional one. A physical model for temperature testing in the magnetic bearing has been developed. Some results obtained from computer simulations were compared with measurements.

scholarly journals IMAGE ENCRYPTION BASED ON TWO-DIMENSIONAL FRACTIONAL QUADRIC POLYNOMIAL MAP

Fractals ◽  
2021 ◽  
pp. 2140041
Author(s):  
ZE-YU LIU ◽  
TIE-CHENG XIA ◽  
HUA-RONG FENG ◽  
CHANG-YOU MA
Keyword(s):  
Image Encryption ◽  
Color Image ◽  
Chaotic Map ◽  
Encryption Algorithm ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Two Dimensional ◽  
Polynomial Map ◽  
Dynamical Behaviors ◽  
Image Encryption Algorithm

A new fractional two-dimensional quadric polynomial discrete chaotic map (2D-QPDM) with the discrete fractional difference is proposed. Afterwards, the new dynamical behaviors are observed, so that the bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits of the proposed map are given, respectively. The new discrete fractional map is exploited into color image encryption algorithm and it is illustrated with several examples. The proposed image encryption algorithm is analyzed in six aspects which indicates that the proposed algorithm is superior to other known algorithms as a conclusion.

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.

BIFURCATION AND CHAOS IN THE TINKERBELL MAP

2011 ◽  
Vol 21 (11) ◽  
pp. 3137-3156 ◽  
Author(s):  
SHAOLIANG YUAN ◽  
TAO JIANG ◽  
ZHUJUN JING
Keyword(s):  
Three Dimensional ◽  
Period Doubling ◽  
Phase Portraits ◽  
Transient Chaos ◽  
Flip Bifurcation ◽  
Maximum Lyapunov Exponent ◽  
Invariant Circle ◽  
Dynamical Behaviors ◽  
Fold Bifurcation ◽  
Period Doubling Bifurcations

In this paper, the dynamical behaviors of the Tinkerbell map are investigated in detail. Conditions for the existence of fold bifurcation, flip bifurcation and Hopf bifurcation are derived, and chaos in the sense of Marotto is verified by both analytical and numerical methods. Numerical simulations include bifurcation diagrams in two- and three-dimensional spaces, phase portraits, and the maximum Lyapunov exponent and fractal dimension, as well as the distribution of dynamics in the parameter plane, which exhibit new and interesting dynamical behaviors. More specifically, this paper reports the findings of chaos in the sense of Marotto, a route from an invariant circle to transient chaos with a great abundance of periodic windows, including period-2, 7, 8, 9, 10, 13, 17, 19, 23, 26 and so on, and suddenly appearing or disappearing chaos, convergence of an invariant circle to a period-one orbit, symmetry-breaking of periodic orbits, interlocking period-doubling bifurcations in chaotic regions, interior crisis, chaotic attractors, coexisting (2, 10, 13) chaotic sets, two coexisting invariant circles, two attracting chaotic sets coexisting with a non-attracting chaotic set, and so on, all in the Tinkerbell map. In particular, it is found that there is no obvious road from period-doubling bifurcations to chaos, but there is a route from a period-one orbit to an invariant circle and then to transient chaos as the parameters are varied. Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding of the Tinkerbell map is obtained.

Heat Transfer by Laminar Natural Convection Within Rectangular Enclosures

1970 ◽  
Vol 92 (1) ◽  
pp. 159-167 ◽  
Author(s):  
M. E. Newell ◽  
F. W. Schmidt
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Three Dimensional ◽  
Time Dependent ◽  
Two Dimensional ◽  
Numerical Techniques ◽  
Grashof Number ◽  
Different Temperatures ◽  
Laminar Natural Convection ◽  
Steady State Solutions

Two-dimensional laminar natural convection in air contained in a long horizontal rectangular enclosure with isothermal walls at different temperatures has been investigated using numerical techniques. The time-dependent governing differential equations were solved using a method based on that of Crank and Nicholson. Steady-state solutions were obtained for height to width ratios of 1, 2.5, 10, and 20, and for values of the Grashof number, GrL′, covering the range 4 × 103 to 1.4 × 105. The bounds on the Grashof number for H/L = 20 is 8 × 103 ≤ GrL′ ≤ 4 × 104. The results were correlated with a three-dimensional power law which, yielded H/L=1Nu¯L′=0.0547(GrL′)0.3972.5≤H/L≤20Nu¯L′=0.155(GrL′)0.315(H/L)−0.265 The results compare favorably with available experimental results.

Nonlinear Dynamics and Chaos

2019 ◽  
pp. 111-153
Author(s):  
David D. Nolte
Keyword(s):  
Nonlinear Dynamics ◽  
State Space ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Phase Portraits ◽  
Two Dimensional ◽  
Floquet Multipliers ◽  
Dimensional State Space ◽  
State Space System

The geometric structure of state space is understood through phase portraits and stability analysis that classify the character of fixed points based on the properties of Lyapunov exponents. Limit cycles are an important type of periodic orbit that occurs in many nonlinear systems, and their stability is analyzed according to Floquet multipliers. When time dependence is added to an autonomous two-dimensional state space system to make it non-autonomous, then chaos can emerge, as in the case of the driven damped pendulum. Autonomous systems with three-dimensional chaos include the Lorenz and Rössler models. Dissipative chaos often displays strange attractors with fractal dimensions.

MODIFIED GENERALIZED LORENZ SYSTEM AND FOLDED CHAOTIC ATTRACTORS

2009 ◽  
Vol 19 (08) ◽  
pp. 2573-2587 ◽  
Author(s):  
BOCHENG BAO ◽  
ZHONG LIU ◽  
JUEBANG YU
Keyword(s):  
Chaotic Systems ◽  
Normal Forms ◽  
Lorenz System ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Generalized Lorenz System ◽  
Parameter Values ◽  
Lyapunov Exponent Spectrum

A modified generalized Lorenz system in a canonical form extended from the generalized Lorenz system is proposed in this paper. This novel system has a folded factor and can display complex 2-scroll folded attractors and 1-scroll folded attractors at different parameter values. Three typical normal forms, called Lorenz-like, Chen-like and Lü-like chaotic system respectively, of three-dimensional quadratic autonomous chaotic systems are derived, and their dynamical behaviors are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincaré mapping and phase portrait, etc. Of particular interest is the fact that the folded factor makes Chen-like and Lü-like chaotic systems exhibit complicated nonlinear dynamical phenomena.

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