scholarly journals Hidden Attractors in a Model of a Bubble Contrast Agent Oscillating Near an Elastic Wall

2018 ◽  
Vol 173 ◽  
pp. 06006 ◽  
Author(s):  
Ivan Garashchuk ◽  
Dmitry Sinelshchikov ◽  
Nikolay Kudryashov
Keyword(s):  
Contrast Agent ◽  
Pressure Field ◽  
Finite Thickness ◽  
External Pressure ◽  
Control Parameters ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Elastic Wall ◽  
Periodic Attractors ◽  
Perpetual Points

A model describing the dynamics of a spherical gas bubble in a compressible viscous liquid is studied. The bubble is oscillating close to an elastic wall of finite thickness under the influence of an external pressure field which simulates a contrast agent oscillating close to a blood vessel wall. Here we investigate numerically the coexistence of chaotic and periodic attractors in this model. One of the tools applied for seeking coexisting attractors is the perpetual points method. This method can be helpful for localizing coexisting attractors, occurring in various physically realistic ranges of variation of the control parameters. We provide some examples of coexisting attractors to demonstrate the importance of the multistability problem for the applications.

Acoustic scattering from a contrast agent microbubble near an elastic wall of finite thickness

2011 ◽  
Vol 56 (21) ◽  
pp. 6951-6967 ◽  
Author(s):  
Alexander A Doinikov ◽  
Leila Aired ◽  
Ayache Bouakaz
Keyword(s):  
Contrast Agent ◽  
Finite Thickness ◽  
Acoustic Scattering ◽  
Elastic Wall

scholarly journals Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Qiang Lai ◽  
Paul Didier Kamdem Kuate ◽  
Huiqin Pei ◽  
Hilaire Fotsin
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Physical Meaning ◽  
Control Method ◽  
Initial Conditions ◽  
Periodic Motions ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Dynamic Behaviors

This paper proposes a new no-equilibrium chaotic system that has the ability to yield infinitely many coexisting hidden attractors. Dynamic behaviors of the system with respect to the parameters and initial conditions are numerically studied. It shows that the system has chaotic, quasiperiodic, and periodic motions for different parameters and coexists with a large number of hidden attractors for different initial conditions. The circuit and microcontroller implementations of the system are given for illustrating its physical meaning. Also, the synchronization conditions of the system are established based on the adaptive control method.

scholarly journals Composite One- to Six-Scroll Hidden Attractors in a Memristor-Based Chaotic System and Their Circuit Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ying Li ◽  
Xiaozhu Xia ◽  
Yicheng Zeng ◽  
Qinghui Hong
Keyword(s):  
Fixed Point ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Different Types ◽  
Hardware Circuit ◽  
New System

Chaotic systems with hidden multiscroll attractors have received much attention in recent years. However, most parts of hidden multiscroll attractors previously reported were repeated by the same type of attractor, and the composite of different types of attractors appeared rarely. In this paper, a memristor-based chaotic system, which can generate composite attractors with one up to six scrolls, is proposed. These composite attractors have different forms, similar to the Chua’s double scroll and jerk double scroll. Through theoretical analysis, we find that the new system has no fixed point; that is to say, all of the composite multiscroll attractors are hidden attractors. Additionally, some complicated dynamic behaviors including various hidden coexisting attractors, extreme multistability, and transient transition are explored. Moreover, hardware circuit using discrete components is implemented, and its experimental results supported the numerical simulations results.

Multistability Control of Hysteresis and Parallel Bifurcation Branches through a Linear Augmentation Scheme

2019 ◽  
Vol 75 (1) ◽  
pp. 11-21 ◽  
Author(s):  
T. Fonzin Fozin ◽  
G. D. Leutcho ◽  
A. Tchagna Kouanou ◽  
G. B. Tanekou ◽  
R. Kengne ◽  
...  
Keyword(s):  
Coupling Parameter ◽  
Phase Portraits ◽  
Coexisting Attractors ◽  
Nonlinear Dynamical ◽  
Numerical Investigations ◽  
System Parameters ◽  
Chua’S Oscillator ◽  
Control Scheme ◽  
Periodic Attractors ◽  
Basin Of Attractions

AbstractMultistability analysis has received intensive attention in recently, however, its control in systems with more than two coexisting attractors are still to be discovered. This paper reports numerically the multistability control of five disconnected attractors in a self-excited simplified hyperchaotic canonical Chua’s oscillator (hereafter referred to as SHCCO) using a linear augmentation scheme. Such a method is appropriate in the case where system parameters are inaccessible. The five distinct attractors are uncovered through the combination of hysteresis and parallel bifurcation techniques. The effectiveness of the applied control scheme is revealed through the nonlinear dynamical tools including bifurcation diagrams, Lyapunov’s exponent spectrum, phase portraits and a cross section basin of attractions. The results of such numerical investigations revealed that the asymmetric pair of chaotic and periodic attractors which were coexisting with the symmetric periodic one in the SHCCO are progressively annihilated as the coupling parameter is increasing. Monostability is achieved in the system through three main crises. First, the two asymmetric periodic attractors are annihilated through an interior crisis after which only three attractors survive in the system. Then, comes a boundary crisis which leads to the disappearance of the symmetric attractor in the system. Finally, through a symmetry restoring crisis, a unique symmetric attractor is obtained for higher values of the control parameter and the system is now monostable.

A Novel Simple Hyperchaotic System with Two Coexisting Attractors

2019 ◽  
Vol 29 (14) ◽  
pp. 1950203 ◽  
Author(s):  
Jiaopeng Yang ◽  
Zhengrong Liu
Keyword(s):  
Complex Dynamics ◽  
Chaotic Dynamic ◽  
Cross Product ◽  
Hyperchaotic System ◽  
Compound Structure ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Periodic Attractors ◽  
New Hyperchaotic System ◽  
New System

This article introduces a new hyperchaotic system of four-dimensional autonomous ordinary differential equations, with only cubic cross-product nonlinearities, which can respectively display two hyperchaotic attractors with only nonhyperbolic equilibria line. Several issues such as basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new hyperchaotic and chaotic system are investigated, either theoretically or numerically. Of particular interest is the fact that the two coexisting attractors of the new hyperchaotic system are symmetrical, and this hyperchaotic system can generate plenty of complex dynamics including two coexisting chaotic or periodic attractors. Moreover, some chaotic features of the attractor are justified numerically. Finally, 0-1 test is used to analyze and describe the complex chaotic dynamic behavior of the new system.

Are Perpetual Points Sufficient for Locating Hidden Attractors?

2017 ◽  
Vol 27 (03) ◽  
pp. 1750037 ◽  
Author(s):  
Fahimeh Nazarimehr ◽  
Batool Saedi ◽  
Sajad Jafari ◽  
J. C. Sprott
Keyword(s):  
Nonlinear Dynamics ◽  
Hidden Attractors ◽  
Perpetual Points

Perpetual Points (PPs) have been introduced as an interesting new topic in nonlinear dynamics, and there is a conjecture that these points can be used to find hidden attractors. This note demonstrates some examples where PPs cannot locate their hidden attractors.

scholarly journals A New Megastable Chaotic Oscillator with Blinking Oscillation terms

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Dhinakaran Veeman ◽  
Hayder Natiq ◽  
Nadia M. G. Al-Saidi ◽  
Karthikeyan Rajagopal ◽  
Sajad Jafari ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Limit Cycle ◽  
Chaotic Systems ◽  
High Sensitivity ◽  
Sample Entropy ◽  
Chaotic Oscillator ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Initial Values

Recently, megastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems. In this paper, the oscillatory terms’ coefficients of the simplest megastable oscillator are forced to blink in time. The forced system can generate an infinitive number of hidden attractors without changing parameters. The behavior of these hidden attractors can be chaotic, tori, and limit cycle. The attractors’ topology of the system seems unique and looks like picture frames. Besides, the existence of different coexisting attractors with different kinds of behaviors reflects the system's high sensitivity. Using the sample entropy algorithm, the system’s complexity for different initial values is assessed. In addition, the circuit of the introduced forced system is designed, and the possibility of implicating the system with analog elements is investigated.

Dynamical analysis, FPGA implementation and synchronization for secure communication of new chaotic system with hidden and coexisting attractors

2021 ◽  
Author(s):  
Qiang Lai ◽  
Ziling Wang ◽  
Paul Didier Kamdem Kuate
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Analog Circuit ◽  
Control Method ◽  
Simulation Analysis ◽  
Period Doubling ◽  
Fpga Implementation ◽  
Dynamical Analysis ◽  
Hidden Attractors ◽  
Coexisting Attractors

This paper proposes an interesting autonomous chaotic system with hidden attractors and coexisting attractors. The system has no equilibrium, one equilibrium, three equilibria and line equilibria for different parameter regions. The existence of hidden attractors and coexisting attractors of the system has been revealed by using simulation analysis. The bifurcation diagram shows the period-doubling bifurcation route to chaos with the variation of parameters. The analog circuit and FPGA implementation of the system are presented. The synchronization for secure communication of the system is investigated. The synchronization conditions are established by using the adaptive control method.

A Refinement of the Theory of Buckling of Rings Under Uniform Pressure

1955 ◽  
Vol 22 (1) ◽  
pp. 95-102
Author(s):  
A. P. Boresi
Keyword(s):  
Cross Section ◽  
Classical Result ◽  
Rectangular Cross Section ◽  
Finite Thickness ◽  
Beam Theory ◽  
Elastic Stability ◽  
External Pressure ◽  
Uniform Pressure ◽  
Variational Theory ◽  
Uniform External Pressure

Abstract A general variational theory of elastic stability that was originated by E. Trefftz (1) is applied to the problem of buckling of rings of rectangular cross section subjected to uniform external pressure. The theory is believed to be more rigorous than previous treatments of the problem, since it avoids conventional assumptions of curved-beam theory, such as the assumptions that plane sections remain plane and that radial stresses vanish. The classical result of Levy (2) is confirmed for a ring of infinitesimal thickness. New results are obtained which show the effect of the finite thickness of a ring on the coefficients in the buckling formula.

scholarly journals Wake and wave resistance on viscous thin films

2016 ◽  
Vol 792 ◽  
pp. 829-849 ◽  
Author(s):  
René Ledesma-Alonso ◽  
Michael Benzaquen ◽  
Thomas Salez ◽  
Elie Raphaël
Keyword(s):  
Pressure Field ◽  
Finite Size ◽  
External Source ◽  
External Pressure ◽  
Wave Resistance ◽  
Two Dimensional ◽  
Pressure Source ◽  
One Dimensional ◽  
Speed Up

The effect of an external pressure disturbance, being displaced with a constant speed along the free surface of a viscous thin film, is studied theoretically in the lubrication approximation in one- and two-dimensional geometries. In the comoving frame, the imposed pressure field creates a stationary deformation of the interface – a wake – that spatially vanishes in the far region. The shape of the wake and the way it vanishes depend on both the speed and size of the external source and the properties of the film. The wave resistance, namely the force that has to be externally furnished in order to maintain the wake, is analysed in detail. For finite-size pressure disturbances, it increases with the speed, up to a certain transition value, above which a monotonic decrease occurs. The role of the horizontal extent of the pressure field is studied as well, revealing that for a smaller disturbance the latter transition occurs at a higher speed. Eventually, for a Dirac pressure source, the wave resistance either saturates for a one-dimensional geometry, or diverges for a two-dimensional geometry.

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