scholarly journals Coexisting Oscillation and Extreme Multistability for a Memcapacitor-Based Circuit

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Guangyi Wang ◽  
Chuanbao Shi ◽  
Xiaowei Wang ◽  
Fang Yuan
Keyword(s):  
Limit Cycle ◽  
Infinite Number ◽  
Chaotic Attractor ◽  
Electronic Circuit ◽  
Equilibrium Points ◽  
Experimental Result ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Fix Point ◽  
The Stability

The coexisting oscillations are observed with a memcapacitor-based circuit that consists of two linear inductors, two linear resistors, and an active nonlinear charge-controlled memcapacitor. We analyze the dynamics of this circuit and find that it owns an infinite number of equilibrium points and coexisting attractors, which means extreme multistability arises. Furthermore, we also show the stability of the infinite many equilibria and analyze the coexistence of fix point, limit cycle, and chaotic attractor in detail. Finally, an experimental result of the proposed oscillator via an analog electronic circuit is given.

Bistable and Coexisting Attractors in Current Modulated Edge Emitting Semiconductor Laser: Control and Microcontroller-Based Design

2021 ◽  
Author(s):  
Nasr Saeed ◽  
Serdar Çiçek ◽  
André Cheage Chamgoué ◽  
Sifeu Takougang Kingni ◽  
Zhouchao Wei
Keyword(s):  
Numerical Analysis ◽  
Semiconductor Laser ◽  
Limit Cycle ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Laser Control ◽  
The Stability

Abstract This paper reports on the numerical analysis, control of coexisting attractors and microcontroller-based design of current modulated edge emitting semiconductor laser (CMEESL). The stability of equilibrium points of solitary edge emitting semiconductor laser found is investigated. By varying the amplitude of modulation current density, CMEESL displays periodic behaviors, period-doubling to chaotic behavior, bistability and coexistence between limit cycle and chaotic attractors. The coexistence between chaotic and limit cycle attractors is destroyed and controlled to a desired monostable trajectory by means of the linear augmentation method. In addition, a microcontroller-based circuit is also designed to indicate that CMEESL can be used in real applications. Microcontroller-based circuit outputs and numerical analysis results confirm each other.

Finding Method and Analysis of Hidden Chaotic Attractors for Plasma Chaotic System From Physical and Mechanistic Perspectives

2020 ◽  
Vol 30 (05) ◽  
pp. 2050072 ◽  
Author(s):  
Yingjuan Yang ◽  
Guoyuan Qi ◽  
Jianbing Hu ◽  
Philippe Faradja
Keyword(s):  
Chaotic Attractor ◽  
Equilibrium Points ◽  
Basin Of Attraction ◽  
The Self ◽  
Numerical Continuation ◽  
Chaotic Attractors ◽  
Phase Portrait Analysis ◽  
The Stability ◽  
Two Parameters ◽  
The Basin Of Attraction

A method for finding hidden chaotic attractors in the plasma system is presented. Using the Routh–Hurwitz criterion, the stability distribution associated with two parameters is identified to find the region around the equilibrium points of the stable nodes, stable focus-nodes, saddles and saddle-foci for the purpose of investigating hidden chaos. A physical interpretation is provided of the stability distribution for each type of equilibrium point. The basin of attraction and parameter region of hidden chaos are identified by excluding the self-excited chaotic attractors of all equilibrium points. Homotopy and numerical continuation are also employed to check whether the basin of chaotic attraction intersects with the neighborhood of a saddle equilibrium. Bifurcation analysis, phase portrait analysis, and basins of different dynamical attraction are used as tools to distinguish visually the self-excited chaotic attractor and hidden chaotic attractor. The Casimir power reflects the error power between the dissipative energy and the energy supplied by the whistler field. It explains physically, analytically, and numerically the conditions that generate the different dynamics, such as sinks, periodic orbits, and chaos.

scholarly journals A Chaotic System with Infinite Equilibria and Its S-Box Constructing Application

2018 ◽  
Vol 8 (11) ◽  
pp. 2132 ◽  
Author(s):  
Xiong Wang ◽  
Akif Akgul ◽  
Unal Cavusoglu ◽  
Viet-Thanh Pham ◽  
Duy Vo Hoang ◽  
...  
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Electronic Circuit ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Performance Tests ◽  
Generation Algorithm ◽  
Performance Results ◽  
Number Of Equilibria ◽  
Line Equilibrium

Systems with many equilibrium points have attracted considerable interest recently. A chaotic system with a line equilibrium has been studied in this work. The system has infinite equilibria and exhibits coexisting chaotic attractors. The system with an infinite number of equilibria has been realized by an electronic circuit, which confirms the feasibility of the system. Based on such a system, we have developed a new S-Box generation algorithm. With the developed algorithm, two new S-Boxes are produced. Performance tests of S-Boxes are performed. The tests have shown that proposed S-Boxes have good performance results.

Antimonotonicity, Bifurcation and Multistability in the Vallis Model for El Niño

2019 ◽  
Vol 29 (03) ◽  
pp. 1950032 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
Zhouchao Wei ◽  
Durairaj Premraj ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
El Niño ◽  
El Nino ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Coexisting Attractors ◽  
The Stability ◽  
First Time ◽  
Parameter Condition

In this paper, the well-known Vallis model for El Niño is analyzed for the parameter condition [Formula: see text]. The conditions for the stability of the equilibrium points are derived. The condition for Hopf bifurcation occurring in the system for [Formula: see text] and [Formula: see text] are investigated. The multistability feature of the Vallis model when [Formula: see text] is explained with forward and backward continuation bifurcation plots and with the coexisting attractors. The creation of period doubling followed by their annihilation via inverse period-doubling bifurcation known as antimonotonicity occurrence in the Vallis model for [Formula: see text] is presented for the first time in the literature.

A Chaotic System with Different Shapes of Equilibria

2016 ◽  
Vol 26 (04) ◽  
pp. 1650069 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Sajad Jafari ◽  
Xiong Wang ◽  
Jun Ma
Keyword(s):  
Infinite Number ◽  
Chaotic Attractor ◽  
Chaotic Systems ◽  
Current Knowledge ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Dimensional System ◽  
Different Shapes ◽  
Number Of Equilibria ◽  
Three Dimensional System

Although many chaotic systems have been introduced in the literature, a few of them possess uncountably infinite equilibrium points. The aim of our short work is to widen the current knowledge of the chaotic systems with an infinite number of equilibria. A three-dimensional system with special properties, for example, exhibiting chaotic attractor with circular equilibrium, chaotic attractor with ellipse equilibrium, chaotic attractor with square-shaped equilibrium, and chaotic attractor with rectangle-shaped equilibrium, is proposed.

Symmetric coexisting attractors and extreme multistability in chaotic system

2021 ◽  
pp. 2150458
Author(s):  
Xiaoxia Li ◽  
Chi Zheng ◽  
Xue Wang ◽  
Yingzi Cao ◽  
Guizhi Xu
Keyword(s):  
Chaotic System ◽  
Electronic Circuit ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
New Chaotic System ◽  
Initial States ◽  
Parameter Ranges ◽  
New System

In this paper, a new four-dimensional (4D) chaotic system with two cubic nonlinear terms is proposed. The most striking feature is that the new system can exhibit completely symmetric coexisting bifurcation behaviors and four symmetric coexisting attractors with the same Lyapunov exponents in all parameter ranges of the system when taking different initial states. Interestingly, these symmetric coexisting attractors can be considered as unusual symmetrical rotational coexisting attractors, which is a very fascinating phenomenon. Furthermore, by using a memristor to replace the coupling resistor of the new system, an interesting 4D memristive hyperchaotic system with one unstable origin is constructed. Of particular surprise is that it can exhibit four groups of extreme multistability phenomenon of infinitely many coexisting attractors of symmetric distribution about the origin. By using phase portraits, Lyapunov exponent spectra, and coexisting bifurcation diagrams, the dynamics of the two systems are fully analyzed and investigated. Finally, the electronic circuit model of the new system is designed for verifying the feasibility of the new chaotic system.

MULTISTABILITY IN A BUTTERFLY FLOW

2013 ◽  
Vol 23 (12) ◽  
pp. 1350199 ◽  
Author(s):  
CHUNBIAO LI ◽  
J. C. SPROTT
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Fractal Structure ◽  
Equilibrium Points ◽  
Symmetric Pair ◽  
Coexisting Attractors ◽  
Quadratic Nonlinearities ◽  
Stable Equilibria ◽  
Basin Boundaries ◽  
Special Parameter

A dynamical system with four quadratic nonlinearities is found to display a butterfly strange attractor. In a relatively large region of parameter space the system has coexisting point attractors and limit cycles. At some special parameter combinations, there are five coexisting attractors, where a limit cycle coexists with two equilibrium points and two strange attractors in different attractor basins. The basin boundaries have a symmetric fractal structure. In addition, the system has other multistable regimes where a pair of point attractors coexist with a single limit cycle or a symmetric pair of limit cycles and where a symmetric pair of limit cycles coexist without any stable equilibria.

scholarly journals Bifurcations of a New Fractional-Order System with a One-Scroll Chaotic Attractor

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Lixin Yang ◽  
Dafeng Tang
Keyword(s):  
Fractional Order ◽  
Chaotic Attractor ◽  
System Parameter ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Order System ◽  
Order Case ◽  
The Stability ◽  
The One ◽  
Derivative Order

In this paper, a new fractional-order system which has a chaotic attractor of the one-scroll structure is presented. Firstly, the stability of the equilibrium points of the system is investigated. And based on the stability analysis, the generation conditions of the one-scroll structure for the attractor are determined. In a commensurate-order case, bifurcations with the variation of a system parameter are investigated as derivative orders decrease from 0.99. In an incommensurate-order case, bifurcations with the variation of a derivative order are analyzed as other orders decrease from 1.

The Stability and Chaotic Motions of a Four-Wing Chaotic Attractor

2011 ◽  
Vol 48-49 ◽  
pp. 1315-1318 ◽  
Author(s):  
Xia Wang ◽  
Jian Ping Li ◽  
Jian Yin Fang
Keyword(s):  
Chaotic Attractor ◽  
Autonomous System ◽  
Equilibrium Points ◽  
Heteroclinic Orbits ◽  
Series Expansions ◽  
Chaotic Motions ◽  
Undetermined Coefficient ◽  
The Stability ◽  
Coefficient Method ◽  
Undetermined Coefficient Method

The stability and chaotic motions of a 3-D quadratic autonomous system with a four-wing chaotic attractor are investigated in this paper. Base on the linearization analysis, the stability of the equilibrium points is studied. By using the undetermined coefficient method, the heteroclinic orbits are found and the convergence of the series expansions of this type of orbits is proved. It analytically demonstrates that there exist heteroclinic orbits of Silnikov type connecting the equilibrium points. Therefore, Smale horseshoes and the horseshoe chaos occur for this system via the Silnikov criterion.

scholarly journals Network Dynamics of a Fractional-Order Phase-Locked Loop with Infinite Coexisting Attractors

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Anitha Karthikeyan ◽  
Karthikeyan Rajagopal
Keyword(s):  
Fractional Order ◽  
Large Scale ◽  
Equilibrium Points ◽  
Network Dynamics ◽  
Phase Locked Loop ◽  
Coexisting Attractors ◽  
Third Order ◽  
Large Scale Networks ◽  
The Stability ◽  
Multiple Coexisting Attractors

We have investigated a fractional-order phase-locked loop characterised by a third-order differential equation. The integer-order mathematical model of the phase-locked loop (PLL) is first converted to fractional order using the Caputo-Fabrizio method. The stability of the equilibrium points is discussed in detail in both parameter and fractional-order domain. The proposed fractional-order phase-locked loop (FOPLL) model shows multiple coexisting attractors which was not discussed in the earlier literature of PLL. The significance of these infinite coexisting attractors is that they exist in the operation region of the PLL between [−π,π] which increases the complexity of operation of the PLLs. Mainly when such FOPLLs are used in large-scale networks, the synchronisation of the FOPLLs becomes complicated and will result in unstable control conditions. Hence, studying the network dynamics of such FOPLLs is significant which motivates us to investigate the synchronisation phenomenon of the FOPLLs constructed in a square network. We could show that, because of the multiple coexisting attractors, the FOPLLs show various synchronisation phenomena, and more importantly in the chaotic region for lower fractional-order values, we could show that the FOPLLs are synchronised and this finding is very useful to completely analyse the FOPLL networks in high-frequency operations.

Sign in / Sign up

Export Citation Format

Share Document