A New Multi-Scroll Megastable Oscillator Based on the Sign Function

2021 ◽  
Vol 31 (08) ◽  
pp. 2150140
Author(s):  
Haikong Lu ◽  
Karthikeyan Rajagopal ◽  
Fahimeh Nazarimehr ◽  
Sajad Jafari
Keyword(s):  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Periodic Excitation ◽  
Sign Function ◽  
Initial Values ◽  
Dynamical Properties ◽  
Parameter Values

A chaotic system that can show multiscroll and megastable attractors is studied in this paper. Two cases of the system with periodic and quasi-periodic excitations are discussed. Various stabilities of the system determined by changing parameters and initial values are investigated for both cases. In Case-A of the proposed system, multiscroll attractors are shown for the various parameter values. In Case-B with quasi-periodic excitation, the system shows various multiscroll attractors. Dynamical properties of these two cases are studied using the bifurcation diagram and Lyapunov exponents.

A New Imprisoned Strange Attractor

2019 ◽  
Vol 29 (13) ◽  
pp. 1950181
Author(s):  
Fahimeh Nazarimehr ◽  
Viet-Thanh Pham ◽  
Karthikeyan Rajagopal ◽  
Fawaz E. Alsaadi ◽  
Tasawar Hayat ◽  
...  
Keyword(s):  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Strange Attractor ◽  
Period Doubling ◽  
Chaotic Attractors ◽  
Spherical Coordinate ◽  
New Chaotic System ◽  
Route To Chaos ◽  
Dynamical Properties

This paper proposes a new chaotic system with a specific attractor which is bounded in a sphere. The system is offered in the spherical coordinate. Dynamical properties of the system are investigated in this paper. The system shows multistability, and all of its attractors are inside or on the surface of the specific sphere. Bifurcation diagram of the system displays an inverse period-doubling route to chaos. Lyapunov exponents of the system are studied to show its chaotic attractors and predict its bifurcation points.

A New Chaotic Dynamic System Research

2013 ◽  
Vol 392 ◽  
pp. 227-231
Author(s):  
Gui Qing Zhao ◽  
Guo Zeng Wu
Keyword(s):  
Dynamic System ◽  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Phase Plane ◽  
Chaotic Dynamic ◽  
System Research ◽  
And Topology ◽  
Dynamical Properties

A new four-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. It is a new phenomenon that the phase plane attractors can achieve opposite and topology of exactly by changing the parameter symbol of c.

Two Simplest Quadratic Chaotic Maps Without Equilibrium

2018 ◽  
Vol 28 (12) ◽  
pp. 1850144 ◽  
Author(s):  
Shirin Panahi ◽  
Julien C. Sprott ◽  
Sajad Jafari
Keyword(s):  
Dynamical System ◽  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic Maps ◽  
Basin Of Attraction ◽  
Hidden Attractor ◽  
Return Map ◽  
Right Hand ◽  
Dynamical Properties ◽  
The Right

Two simple chaotic maps without equilibria are proposed in this paper. All nonlinearities are quadratic and the functions of the right-hand side of the equations are continuous. The procedure of their design is explained and their dynamical properties such as return map, bifurcation diagram, Lyapunov exponents, and basin of attraction are investigated. These maps belong to the hidden attractor category which is a newly introduced category of dynamical system.

A New Dynamic System Analysis

2013 ◽  
Vol 392 ◽  
pp. 222-226
Author(s):  
Bao Liang Mi ◽  
Guo Zeng Wu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Dynamic System ◽  
Bifurcation Diagram ◽  
Chaotic System ◽  
System Analysis ◽  
Electronic Circuit ◽  
Circuit Implementation ◽  
Dynamical Properties ◽  
Electronic Circuit Implementation

A new four-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit implementation.

Constructing a Novel No-Equilibrium Chaotic System

2014 ◽  
Vol 24 (05) ◽  
pp. 1450073 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Zhouchao Wei ◽  
Xiong Wang
Keyword(s):  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Poincaré Map ◽  
Period Doubling ◽  
Circuit Realization ◽  
Chaotic Flow ◽  
Route To Chaos ◽  
Line Equilibrium

This paper introduces a new no-equilibrium chaotic system that is constructed by adding a tiny perturbation to a simple chaotic flow having a line equilibrium. The dynamics of the proposed system are investigated through Lyapunov exponents, bifurcation diagram, Poincaré map and period-doubling route to chaos. A circuit realization is also represented. Moreover, two other new chaotic systems without equilibria are also proposed by applying the presented methodology.

scholarly journals A New Four-Scroll Chaotic Attractor Consisted of Two-Scroll Transient Chaotic and Two-Scroll Ultimate Chaotic

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yuhua Xu ◽  
Bing Li ◽  
Yuling Wang ◽  
Wuneng Zhou ◽  
Jian-an Fang
Keyword(s):  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
The Other ◽  
Phase Portraits ◽  
Fractional Dimension ◽  
The Novel ◽  
New Chaotic System ◽  
New System

A new four-scroll chaotic attractor is found by feedback controlling method in this paper. The novel chaotic system can generate four scrolls two of which are transient chaotic and the other two of which are ultimate chaotic. Of particular interest is that this novel chaotic system can generate one-scroll, two 2-scroll and four-scroll chaotic attractor with variation of a single parameter. We analyze the new system by means of phase portraits, Lyapunov exponents, fractional dimension, bifurcation diagram, and Poincaré map, respectively. The analysis results show clearly that this is a new chaotic system which deserves further detailed investigation.

A HYPERCHAOTIC SYSTEM WITH A FOUR-WING ATTRACTOR

2009 ◽  
Vol 20 (02) ◽  
pp. 323-335 ◽  
Author(s):  
GUOSI HU ◽  
BO YU
Keyword(s):  
System Dynamics ◽  
Lyapunov Exponents ◽  
Computer Simulations ◽  
Chaotic System ◽  
Bifurcation Analysis ◽  
Topological Structure ◽  
Hyperchaotic System ◽  
Wide Range ◽  
New Chaotic System

Recently, there are many methods for constructing multi-wing/multi-scroll or hyperchaotic attractors; however, it has been noticed that the attractors with both multi-wing topological structure and hyperchaotic characteristic rarely exist. A new chaotic system, obtained by making the change on coordinate to the Hu chaotic system, can generate very complex attractors with four-wing topological structure and three positive Lyapunov exponents over a wide range of parameters. The influence of parameters varying to system dynamics is analyzed, computer simulations and bifurcation analysis is also verified in this paper.

MUTUAL AND SELF-COMPOUNDING OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 759-767
Author(s):  
R. SINGH ◽  
P.S. MOHARIR ◽  
V.M. MARU
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Dynamic Systems ◽  
Mantle Convection ◽  
Chaotic Systems ◽  
Compound System ◽  
Two Systems

The notion of compounding a chaotic system was introduced earlier. It consisted of varying the parameters of the compoundee system in proportion to the variables of the compounder system, resulting in a compound system which has in general higher Lyapunov exponents. Here, the notion is extended to self-compounding of a system with a real-earth example, and mutual compounding of dynamic systems. In the former, the variables in a system perturb its parameters. In the latter, two systems affect the parameters of each other in proportion to their variables. Examples of systems in such compounding relationships are studied. The existence of self-compounding is indicated in the geodynamics of mantle convection. The effect of mutual compounding is studied in terms of Lyapunov exponent variations.

scholarly journals Hybrid Passivity Based and Fuzzy Type-2 Controller for Chaotic and Hyper-Chaotic Systems

2017 ◽  
Vol 11 (2) ◽  
pp. 96-103 ◽  
Author(s):  
Fernando Serrano ◽  
Josep M. Rossell
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Control Law ◽  
Four Dimensions ◽  
Design Requirements ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyper-chaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropriate controller that meets the design requirements. Finally, numerical simulations are done to corroborate the obtained theoretical results.

scholarly journals Generation of 3-D Grid Multi-Scroll Chaotic Attractors Based on Sign Function and Sine Function

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2145
Author(s):  
Pengfei Ding ◽  
Xiaoyi Feng ◽  
Lin Fa
Keyword(s):  
Chaotic System ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Time Shift ◽  
Chaotic Attractors ◽  
Sine Function ◽  
Sign Function ◽  
Simulation Results ◽  
Jerk System ◽  
Lyapunov Exponent Spectrum

A three directional (3-D) multi-scroll chaotic attractors based on the Jerk system with nonlinearity of the sine function and sign function is introduced in this paper. The scrolls in the X-direction are generated by the sine function, which is a modified sine function (MSF). In addition, the scrolls in Y and Z directions are generated by the sign function series, which are the superposition of some sign functions with different time-shift values. In the X-direction, the scroll number is adjusted by changing the comparative voltages of the MSF, and the ones in Y and Z directions are regulated by the sign function. The basic dynamics of Lyapunov exponent spectrum, phase diagrams, bifurcation diagram and equilibrium points distribution were studied. Furthermore, the circuits of the chaotic system are designed by Multisim10, and the circuit simulation results indicate the feasibility of the proposed chaotic system for generating chaotic attractors. On the basis of the circuit simulations, the hardware circuits of the system are designed for experimental verification. The experimental results match with the circuit simulation results, this powerfully proves the correctness and feasibility of the proposed system for generating 3-D grid multi-scroll chaotic attractors.

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