Dynamics of Attractively and Repulsively Coupled Elementary Chaotic Systems

2016 ◽  
Vol 26 (03) ◽  
pp. 1630005
Author(s):  
Sarah Trinschek ◽  
Stefan J. Linz
Keyword(s):  
Chaotic Systems ◽  
Dynamical Behavior ◽  
Coupling Mechanism ◽  
Amplitude Death ◽  
Elementary Model ◽  
Chaotic Flows ◽  
Coupling Strengths ◽  
Jerky Dynamics ◽  
Coupling Mechanisms ◽  
Electronic Implementation

We investigate an elementary model for doubly coupled dynamical systems that consists of two identical, mutually interacting minimal chaotic flows in the form of jerky dynamics. The coupling mechanisms allow for the simultaneous presence of attractive and repulsive interactions between the systems. Despite its functional simplicity, the model is capable of exhibiting diverse types of dynamical phenomena induced by the presence of the couplings. We provide an in-depth numerical investigation of the dynamics depending on the coupling strengths and the autonomous dynamical behavior of the subsystems. Partly, the dynamics of the system can be analytically understood using the Poincaré–Lindstedt method. An approximation of periodic orbits is carried out in the vicinity of a phase-flip transition that leads to deeper insights into the organization of the appearing dynamics in the parameter space. In addition, we propose a circuit that enables an electronic implementation of the model. A variation of the coupling mechanism to a coupling in conjugate variables leads to a regime of amplitude death.

A New Category of Three-Dimensional Chaotic Flows with Identical Eigenvalues

2020 ◽  
Vol 30 (02) ◽  
pp. 2050026 ◽  
Author(s):  
Zahra Faghani ◽  
Fahimeh Nazarimehr ◽  
Sajad Jafari ◽  
Julien C. Sprott
Keyword(s):  
Chaotic Systems ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Special Property ◽  
Computer Search ◽  
Chaotic Flows ◽  
Stable Equilibria ◽  
Dynamical Properties ◽  
Simple Systems ◽  
First Time

In this paper, some new three-dimensional chaotic systems are proposed. The special property of these autonomous systems is their identical eigenvalues. The systems are designed based on the general form of quadratic jerk systems with 10 terms, and some systems with stable equilibria. Using a systematic computer search, 12 simple chaotic systems with identical eigenvalues were found. We believe that systems with identical eigenvalues are described here for the first time. These simple systems are listed in this paper, and their dynamical properties are investigated.

Optimal Synchronization of a Memristive Chaotic Circuit

2016 ◽  
Vol 26 (06) ◽  
pp. 1650093 ◽  
Author(s):  
Michaux Kountchou ◽  
Patrick Louodop ◽  
Samuel Bowong ◽  
Hilaire Fotsin ◽  
Jurgen Kurths
Keyword(s):  
Numerical Simulations ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Analog Circuit ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Dynamical Properties ◽  
Analog Circuit Implementation

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

scholarly journals HOW CRUCIAL IS SMALL WORLD CONNECTIVITY FOR DYNAMICS?

2006 ◽  
Vol 16 (09) ◽  
pp. 2767-2775 ◽  
Author(s):  
PRASHANT M. GADE ◽  
SUDESHNA SINHA
Keyword(s):  
Spectral Properties ◽  
Chaotic Systems ◽  
Signal To Noise Ratio ◽  
Dynamical Behavior ◽  
Small World ◽  
High Strength ◽  
Nonlocal Coupling ◽  
Small Noise ◽  
Optimal Value ◽  
Neuronal Systems

We study the dynamical behavior of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties occur only at a reasonably high strength of nonlocal coupling. Further, spectral features, such as signal-to-noise ratio (SNR), change monotonically with respect to the fraction of random rewiring, i.e. there is no optimal value of the rewiring fraction for which spectral properties are most pronounced. We also observe that for small rewiring, results are similar to those obtained by adding small noise.

Type Synthesis of a 1T Symmetric Coupling Mechanism with the Method of Separation and Merger

2014 ◽  
Vol 635-637 ◽  
pp. 1290-1293
Author(s):  
Shou Li Zhang ◽  
Jing Fang Liu ◽  
Yue Qing Yu
Keyword(s):  
Linear Combination ◽  
Parallel Mechanism ◽  
Creative Design ◽  
Coupling Mechanism ◽  
Type Synthesis ◽  
Structural Synthesis ◽  
Hybrid Mechanism ◽  
Coupled Structures ◽  
Coupling Mechanisms

The structural synthesis is the primary and the most important issue in the process of mechanism creative design. In the paper, Firstly, select a 1T symmetric parallel mechanism, and the constraint and mobility of the branches can be analyzed. With the method of linear combination of the screws, the new branches are constructed. Then, using the measure of separation and merger, parts of the limbs of the parallel mechanism can be replaced by equivalent coupled structures, so corresponding symmetric coupling mechanisms with equal mobility are synthesized. Finally, solving the constraint screws of the branch of the coupling mechanism, in order to prove the hybrid mechanism is full-cycle or not.

Jacobi Stability of Simple Chaotic Systems with One Lyapunov Stable Equilibrium

2021 ◽  
Author(s):  
Changzhi Li ◽  
Biyu Chen ◽  
Aimin Liu ◽  
Huanhuan Tian
Keyword(s):  
Chaotic Systems ◽  
Stable Equilibrium ◽  
Geometrical Structure ◽  
Chaotic Behavior ◽  
Internal Environment ◽  
Small Perturbations ◽  
Chaotic Flows ◽  
Dynamical Behaviors ◽  
Onset Of Chaos ◽  
Deviation Vector

Abstract This paper presents Jacobi stability analysis of 23 simple chaotic systems with only one Lyapunov stable equilibrium by Kosambi-Cartan-Chern (KCC) theory, and analyzes the chaotic behavior of these systems from the geometric viewpoint. Different from Lyapunov stability, the unique equilibrium for each system is always Jacobi unstable. Moreover, the dynamical behaviors of deviation vector near equilibrium are discussed to reveal the onset of chaos for these 23 systems, and show furtherly the coexistence of unique Lyapunov stable equilibrium and chaotic attractor for each system geometrically. The obtaining results show that these chaotic systems are not robust to small perturbations of the equilibrium, indicating that the systems are extremely sensitive to internal environment. This reveals that the chaotic flows generated by these systems may be related to Jacobi instability of the equilibrium. It is hoped that the study of this paper can help reveal the true geometrical structure of hidden chaotic attractors.

The Relationship Between Chaotic Maps and Some Chaotic Systems with Hidden Attractors

2016 ◽  
Vol 26 (13) ◽  
pp. 1650211 ◽  
Author(s):  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
S. Mohammad Reza Hashemi Golpayegani ◽  
Motahareh Moghtadaei ◽  
Sifeu Takougang Kingni
Keyword(s):  
Bifurcation Diagram ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Period Doubling ◽  
Hidden Attractors ◽  
Chaotic Flows ◽  
The Relationship

In this note, hidden attractors in chaotic maps are investigated. Although there are many new researches on hidden attractors in chaotic flows, no investigation has been done on hidden attractors in maps based on our knowledge. In addition, a new interesting chaotic map with a bifurcation diagram starting from any desired period and then continuing with period doubling is introduced in this paper.

Amplitude death in steadily forced chaotic systems

2007 ◽  
Vol 16 (9) ◽  
pp. 2825-2829 ◽  
Author(s):  
Feng Guo-Lin ◽  
He Wen-Ping
Keyword(s):  
Chaotic Systems ◽  
Amplitude Death

The Behavior of Synchronized Frequency in Weakly Coupled Nonidentical Periodic Oscillators

2017 ◽  
Vol 27 (01) ◽  
pp. 1750008
Author(s):  
Priyom Adhyapok ◽  
Mahashweta Patra ◽  
Soumitro Banerjee
Keyword(s):  
Coupled Oscillators ◽  
Chaotic Systems ◽  
Coupled Systems ◽  
Coupling Constant ◽  
Intensive Study ◽  
Amplitude Death ◽  
The Past ◽  
Weakly Coupled ◽  
Simplifying Assumptions ◽  
The Individual

Interaction between dynamical systems has been a subject of intensive study for the past couple of decades. These studies have mainly focused on synchronization of chaotic systems, conditions of different kinds of synchronized behavior, amplitude death, etc. Synchronization of periodic oscillators and the frequency of the resulting synchronized behavior have remained relatively unexplored. In this paper we consider synchronization of nonidentical periodic oscillators for different coupling schemes, and study the nature of the synchronized frequency. Based on numerical and experimental observations we show that for directly coupled oscillators, the synchronized frequency lies between the individual frequencies and its value does not depend on the coupling constant, while for indirectly coupled oscillators the synchronized frequency lies out of the range and depends on the strength of coupling. We explain the different frequency behaviors of directly and indirectly coupled systems by analytically deriving the expressions of synchronized frequency under certain simplifying assumptions.

Multiscroll Chaotic Sea Obtained from a Simple 3D System Without Equilibrium

2016 ◽  
Vol 26 (02) ◽  
pp. 1650031 ◽  
Author(s):  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
Tomasz Kapitaniak
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Exponents ◽  
Chaotic Systems ◽  
Poincaré Map ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Equilibrium System ◽  
Frequency Spectra ◽  
Chaotic Flows ◽  
New System

Recently, many rare chaotic systems have been found including chaotic systems with no equilibria. However, it is surprising that such a system can exhibit multiscroll chaotic sea. In this paper, a novel no-equilibrium system with multiscroll hidden chaotic sea is introduced. Besides having multiscroll chaotic sea, this system has two more interesting properties. Firstly, it is conservative (which is a rare feature in three-dimensional chaotic flows) but not Hamiltonian. Secondly, it has a coexisting set of nested tori. There is a hidden torus which coexists with the chaotic sea. This new system is investigated through numerical simulations such as phase portraits, Lyapunov exponents, Poincaré map, and frequency spectra. Furthermore, the feasibility of such a system is verified through circuital implementation.

scholarly journals The Tension-Twist Coupling Mechanism in Flexible Composites: A Systematic Study Based on Tailored Laminate Structures Using a Novel Test Device

Polymers ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2780 ◽  
Author(s):  
Julia Beter ◽  
Bernd Schrittesser ◽  
Gerald Meier ◽  
Bernhard Lechner ◽  
Mohammad Mansouri ◽  
...  
Keyword(s):  
Coupling Effect ◽  
Coupling Mechanism ◽  
Test Plan ◽  
Test Device ◽  
Reliable Determination ◽  
Flexible Composites ◽  
Number Of Layers ◽  
Symmetric Deformation ◽  
Coupling Mechanisms

The focus of this research is to quantify the effect of load-coupling mechanisms in anisotropic composites with distinct flexibility. In this context, the study aims to realize a novel testing device to investigate tension-twist coupling effects. This test setup includes a modified gripping system to handle composites with stiff fibers but hyperelastic elastomeric matrices. The verification was done with a special test plan considering a glass textile as reinforcing with different lay-ups to analyze the number of layers and the influence of various fiber orientations onto the load-coupled properties. The results demonstrated that the tension-twist coupling effect strongly depends on both the fiber orientation and the considered reinforcing structure. This enables twisting angles up to 25° with corresponding torque of about 82.3 Nmm, which is even achievable for small lay-ups with 30°/60° oriented composites with distinct asymmetric deformation. For lay-ups with ±45° oriented composites revealing a symmetric deformation lead, as expected, no tension-twist coupling effect was seen. Overall, these findings reveal that the described novel test device provides the basis for an adequate and reliable determination of the load-coupled material properties between stiff fibers and hyperelastic matrices.

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