scholarly journals Complex Dynamics in a Memcapacitor-Based Circuit

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 188 ◽  
Author(s):  
Fang Yuan ◽  
Yuxia Li ◽  
Guangyi Wang ◽  
Gang Dou ◽  
Guanrong Chen
Keyword(s):  
Complex System ◽  
Lyapunov Exponents ◽  
Dynamic Characteristics ◽  
Complex Dynamics ◽  
Basins Of Attraction ◽  
Chaotic Oscillator ◽  
Initial Condition ◽  
Circuit Implementation ◽  
Coexisting Attractors ◽  
Extreme Multistability

In this paper, a new memcapacitor model and its corresponding circuit emulator are proposed, based on which, a chaotic oscillator is designed and the system dynamic characteristics are investigated, both analytically and experimentally. Extreme multistability and coexisting attractors are observed in this complex system. The basins of attraction, multistability, bifurcations, Lyapunov exponents, and initial-condition-triggered similar bifurcation are analyzed. Finally, the memcapacitor-based chaotic oscillator is realized via circuit implementation with experimental results presented.

Coexistence of Strange Nonchaotic Attractors in a Quasiperiodically Forced Dynamical Map

2020 ◽  
Vol 30 (13) ◽  
pp. 2050183
Author(s):  
Yunzhu Shen ◽  
Yongxiang Zhang ◽  
Sajad Jafari
Keyword(s):  
Power Spectrum ◽  
Lyapunov Exponents ◽  
Basins Of Attraction ◽  
Initial Condition ◽  
Phase Sensitivity ◽  
Coexisting Attractors ◽  
Sensitive Dependence ◽  
Largest Lyapunov Exponents ◽  
The Creation ◽  
Strange Nonchaotic Attractors

In this paper, we investigate coexisting strange nonchaotic attractors (SNAs) in a quasiperiodically forced system. We also describe the basins of attraction for coexisting attractors and identify the mechanism for the creation of coexisting attractors. We find three types of routes to coexisting SNAs, including intermittent route, Heagy–Hammel route and fractalization route. The mechanisms for the creation of coexisting SNAs are investigated by the interruption of coexisting torus-doubling bifurcations. We characterize SNAs by the largest Lyapunov exponents, phase sensitivity exponents and power spectrum. Besides, the SNAs with extremely fractal basins exhibit sensitive dependence on the initial condition for some particular parameters.

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.

COMPLEX DYNAMICS IN MULTISTABLE SYSTEMS

2008 ◽  
Vol 18 (06) ◽  
pp. 1607-1626 ◽  
Author(s):  
ULRIKE FEUDEL
Keyword(s):  
Complex Dynamics ◽  
Theoretical Models ◽  
Basins Of Attraction ◽  
Stable States ◽  
Coexisting Attractors ◽  
Experimental Systems ◽  
Wide Range ◽  
Multistable Systems

The coexistence of several stable states for a given set of parameters has been observed in many natural and experimental systems as well as in theoretical models. This paper gives an overview over the wide range of applications in different disciplines of science. Furthermore, different system classes possessing multistability are analyzed in terms of the appearance of coexisting attractors and their basins of attraction. It is shown that multistable systems are very sensitive to perturbations leading to a noise-induced hopping process between attractors. The role of chaotic saddles in the escape from attractors in multistable systems is discussed.

BISTABILITY AND DYNAMICAL TRANSITIONS IN A PHASE-MODULATED DELAYED SYSTEM

2009 ◽  
Vol 23 (23) ◽  
pp. 2733-2743 ◽  
Author(s):  
YONGXIANG ZHANG ◽  
GUIQIN KONG ◽  
JIANNING YU
Keyword(s):  
Lyapunov Exponents ◽  
Parameter Space ◽  
Chaotic Dynamics ◽  
Basins Of Attraction ◽  
Parameter Study ◽  
Global Bifurcations ◽  
Coexisting Attractors ◽  
System Parameters ◽  
Different Types ◽  
Delayed System

We study a delayed system with feedback modulation of the nonlinear parameter. Study of the system as a function of nonlinearity and modulation parameters reveals complex dynamical phenomena: different types of coexisting attractors, local or global bifurcations and transitions. Bistability and dynamical attractors can be distinguished in some parameter-space regions, which may be useful to drive chaotic dynamics, unstable attractors or bistability towards regular dynamics. At the bifurcation to bistability, two striking features are that they lead to fundamentally unpredictable behavior of orbits and crisis of attractors as system parameters are varied slowly through the critical curve. Unstable attractors are also investigated in bistable regions, which are easily mistaken for true multi-periodic orbits judging merely from zero measure local basins. Lyapunov exponents and basins of attraction are also used to characterize the phenomenon observed.

Simplest Megastable Chaotic Oscillator

2019 ◽  
Vol 29 (13) ◽  
pp. 1950187 ◽  
Author(s):  
Sajad Jafari ◽  
Karthikeyan Rajagopal ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Viet-Thanh Pham
Keyword(s):  
Nonlinear Dynamics ◽  
Bifurcation Diagram ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Chaotic Oscillator ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Dynamical Properties ◽  
New System

Recently, chaotic systems with hidden attractors and multistability have been of great interest in the field of chaos and nonlinear dynamics. Two special categories of systems with multistability are systems with extreme multistability and systems with megastability. In this paper, the simplest (yet) megastable chaotic oscillator is designed and introduced. Dynamical properties of this new system are completely investigated through tools like bifurcation diagram, Lyapunov exponents, and basin of attraction. It is shown that between its countable infinite coexisting attractors, only one is self-excited and the rest are hidden.

A novel memristor-based chaotic system with line equilibria and its complex dynamics

2021 ◽  
Author(s):  
Dengwei Yan ◽  
Musha Ji’e ◽  
Lidan Wang ◽  
Shukai Duan
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Dynamic Characteristics ◽  
Complex Dynamics ◽  
Circuit Simulation ◽  
Basins Of Attraction ◽  
Maximum Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Structure Complexity ◽  
Complexity Algorithm

Memristor, as a nonlinear element, provides many advantages thanks to its superior properties to design different chaotic circuits. Thus, a novel four-dimensional double-scroll chaotic system with line equilibria as well as two unstable equilibria based on the flux-memristor model is proposed in this paper. The effects of initial values and parameters on the dynamic characteristics of the system are studied in detail by means of phase diagrams, Lyapunov exponent spectrums, bifurcation diagrams, two-parameter bifurcation diagrams and basins of attraction. Besides, a series of complex phenomena in the system, such as sustained chaos, bistability, transient chaos and coexisting attractors are observed, proving that the chaotic system has rich dynamic characteristics. Also, spectral entropy (SE) complexity algorithm and [Formula: see text] complexity algorithm based on structure complexity are adopted to analyze the complexity of the system. Additionally, PSPICE circuit simulation and Micro-Controller Unit (MCU) hardware experiment are carried out to verify the correctness of theoretical analysis and numerical simulation. Finally, the pulse chaos synchronization is achieved from the perspective of maximum Lyapunov exponent, and numerical simulations demonstrate the occurrence of the proposed system and practicability of the pulse synchronization control.

scholarly journals Generating hidden extreme multistability in memristive chaotic oscillator via micro‐perturbation

2018 ◽  
Vol 54 (13) ◽  
pp. 808-810 ◽  
Author(s):  
Lu Wang ◽  
Sen Zhang ◽  
Yi‐Cheng Zeng ◽  
Zhi‐Jun Li
Keyword(s):  
Chaotic Oscillator ◽  
Extreme Multistability ◽  
Hidden Extreme Multistability

Sequences of Global Bifurcations and the Related Outcomes after Crisis of the Resonant Attractor in a Nonlinear Oscillator

1997 ◽  
Vol 07 (11) ◽  
pp. 2437-2457 ◽  
Author(s):  
W. Szemplińska-Stupnicka ◽  
E. Tyrkiel
Keyword(s):  
Nonlinear Oscillator ◽  
Duffing Oscillator ◽  
Nonlinear Resonance ◽  
Basins Of Attraction ◽  
Global Bifurcations ◽  
System Behavior ◽  
Coexisting Attractors ◽  
System Parameters

The problem of the system behavior after annihilation of the resonant attractor in the region of the nonlinear resonance hysteresis is considered. The sequences of global bifurcations, in connection with the associated metamorphoses of basins of attraction of coexisting attractors, are examined. The study allows one to reveal the mechanism that governs the phenomenon of the post crisis ensuing transient trajectory to settle onto one or another remote attractor. The problem is studied in detail for the twin-well potential Duffing oscillator. The boundary which splits the considered region of system parameters into two subdomains, where the outcome is unique or the two outcomes are possible, is defined.

scholarly journals Dynamical Complexity and Multistability in a Novel Lunar Wake Plasma System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Bo. Yan ◽  
Punam K. Prasad ◽  
Sayan Mukherjee ◽  
Asit Saha ◽  
Santo Banerjee
Keyword(s):  
Dynamical System ◽  
Lyapunov Exponents ◽  
Alpha Particles ◽  
Coexisting Attractors ◽  
Plasma System ◽  
Electrostatic Waves ◽  
Lunar Wake ◽  
Dynamical Complexity ◽  
Suprathermal Electrons ◽  
Different Types

Dynamical complexity and multistability of electrostatic waves are investigated in a four-component homogeneous and magnetized lunar wake plasma constituting of beam electrons, heavier ions (alpha particles, He++), protons, and suprathermal electrons. The unperturbed dynamical system of the considered lunar wake plasma supports nonlinear and supernonlinear trajectories which correspond to nonlinear and supernonlinear electrostatic waves. On the contrary, the perturbed dynamical system of lunar wake plasma shows different types of coexisting attractors including periodic, quasiperiodic, and chaotic, investigated by phase plots and Lyapunov exponents. To confirm chaotic and nonchaotic dynamics in the perturbed lunar wake plasma, 0−1 chaos test is performed. Furthermore, a weighted recurrence-based entropy is implemented to investigate the dynamical complexity of the system. Numerical results show existence of chaos with variation of complexity in the perturbed dynamics.

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